Find the value of $int_1^2frac3x-5x^3~dx$.
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up vote
1
down vote
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I want to find the value of
$$int_1^2frac3x-5x^3~dx$$
I'm not sure how to proceed, due to the difference in degree between $3x-5$ and $x^3$. I've tried the substitution $u = 3x-5$, giving the equality
$$int_1^2frac3x-5x^3~dx = 9int_-2^1 fracu(u-5)^3~du$$
However, this doesn't solve the problem I have of the difference in degree between the numerator and the denominator. I thought that perhaps partial fractions would make a difference, but the quadratic I had to solve was untenable.
calculus integration definite-integrals
asked Aug 30 at 1:28
TheAssistant
184
add a comment |Â
up vote
1
down vote
favorite
I want to find the value of
$$int_1^2frac3x-5x^3~dx$$
I'm not sure how to proceed, due to the difference in degree between $3x-5$ and $x^3$. I've tried the substitution $u = 3x-5$, giving the equality
$$int_1^2frac3x-5x^3~dx = 9int_-2^1 fracu(u-5)^3~du$$
However, this doesn't solve the problem I have of the difference in degree between the numerator and the denominator. I thought that perhaps partial fractions would make a difference, but the quadratic I had to solve was untenable.
calculus integration definite-integrals
asked Aug 30 at 1:28
TheAssistant
184
2
Split it and find integeration seperately
– Abhinav
Aug 30 at 1:31
1
While I admittedly made a rather simple mistake here, I'm curious to know where the downvotes are coming from. Is this question not up to quality standards here, outside of the actual math?
– TheAssistant
Aug 30 at 1:39
2
OP, I'm not sure what the downvotes are from. You've demonstrated effort (albeit a simple mistake). I say: Keep up the good work and ask questions as you need to...
– Clayton
Aug 30 at 1:44
Why do you guys downvote ? The OP has posted the question with his/her attempts. I'm not sure why the downvotes are for.
– Ahmad Bazzi
Aug 30 at 2:07
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I want to find the value of
$$int_1^2frac3x-5x^3~dx$$
I'm not sure how to proceed, due to the difference in degree between $3x-5$ and $x^3$. I've tried the substitution $u = 3x-5$, giving the equality
$$int_1^2frac3x-5x^3~dx = 9int_-2^1 fracu(u-5)^3~du$$
However, this doesn't solve the problem I have of the difference in degree between the numerator and the denominator. I thought that perhaps partial fractions would make a difference, but the quadratic I had to solve was untenable.
calculus integration definite-integrals
asked Aug 30 at 1:28
TheAssistant
184
I want to find the value of
$$int_1^2frac3x-5x^3~dx$$
I'm not sure how to proceed, due to the difference in degree between $3x-5$ and $x^3$. I've tried the substitution $u = 3x-5$, giving the equality
$$int_1^2frac3x-5x^3~dx = 9int_-2^1 fracu(u-5)^3~du$$
However, this doesn't solve the problem I have of the difference in degree between the numerator and the denominator. I thought that perhaps partial fractions would make a difference, but the quadratic I had to solve was untenable.
calculus integration definite-integrals
calculus integration definite-integrals
asked Aug 30 at 1:28
TheAssistant
184
asked Aug 30 at 1:28
TheAssistant
184
asked Aug 30 at 1:28
TheAssistant
184
asked Aug 30 at 1:28
TheAssistant
184
asked Aug 30 at 1:28
TheAssistant
184
184
2
Split it and find integeration seperately
– Abhinav
Aug 30 at 1:31
1
While I admittedly made a rather simple mistake here, I'm curious to know where the downvotes are coming from. Is this question not up to quality standards here, outside of the actual math?
– TheAssistant
Aug 30 at 1:39
2
OP, I'm not sure what the downvotes are from. You've demonstrated effort (albeit a simple mistake). I say: Keep up the good work and ask questions as you need to...
– Clayton
Aug 30 at 1:44
Why do you guys downvote ? The OP has posted the question with his/her attempts. I'm not sure why the downvotes are for.
– Ahmad Bazzi
Aug 30 at 2:07
add a comment |Â
2
Split it and find integeration seperately
– Abhinav
Aug 30 at 1:31
1
While I admittedly made a rather simple mistake here, I'm curious to know where the downvotes are coming from. Is this question not up to quality standards here, outside of the actual math?
– TheAssistant
Aug 30 at 1:39
2
OP, I'm not sure what the downvotes are from. You've demonstrated effort (albeit a simple mistake). I say: Keep up the good work and ask questions as you need to...
– Clayton
Aug 30 at 1:44
Why do you guys downvote ? The OP has posted the question with his/her attempts. I'm not sure why the downvotes are for.
– Ahmad Bazzi
Aug 30 at 2:07
2
2
Split it and find integeration seperately
– Abhinav
Aug 30 at 1:31
Split it and find integeration seperately
– Abhinav
Aug 30 at 1:31
1
1
While I admittedly made a rather simple mistake here, I'm curious to know where the downvotes are coming from. Is this question not up to quality standards here, outside of the actual math?
– TheAssistant
Aug 30 at 1:39
While I admittedly made a rather simple mistake here, I'm curious to know where the downvotes are coming from. Is this question not up to quality standards here, outside of the actual math?
– TheAssistant
Aug 30 at 1:39
2
2
OP, I'm not sure what the downvotes are from. You've demonstrated effort (albeit a simple mistake). I say: Keep up the good work and ask questions as you need to...
– Clayton
Aug 30 at 1:44
OP, I'm not sure what the downvotes are from. You've demonstrated effort (albeit a simple mistake). I say: Keep up the good work and ask questions as you need to...
– Clayton
Aug 30 at 1:44
Why do you guys downvote ? The OP has posted the question with his/her attempts. I'm not sure why the downvotes are for.
– Ahmad Bazzi
Aug 30 at 2:07
Why do you guys downvote ? The OP has posted the question with his/her attempts. I'm not sure why the downvotes are for.
– Ahmad Bazzi
Aug 30 at 2:07
add a comment |Â
2 Answers
2
active
oldest
votes
up vote
2
down vote
accepted
Notice that
beginequation
frac3x - 5x^3
=
frac3xx^3
-
frac5x^3
=
frac3x^2
-
frac5x^3
=
3 x^-2 - 5x^-3
endequation
So the integration becomes
beginequation
3 int x^-2 - 5 int x^-3
=
3 fracx^-3-3
-
5
fracx^-4-4
endequation
Can you take it from here ?
answered Aug 30 at 1:32
Ahmad Bazzi
4,9001623
... Somehow I completely convinced myself that I didn't know how to integrate negative powers of $x$. Thanks!
– TheAssistant
Aug 30 at 1:34
1
@TheAssistant: Just remember an exponent of $-1$ needs to be handled differently.
– Clayton
Aug 30 at 1:46
add a comment |Â
up vote
3
down vote
$$int_1^2frac3x-5x^3~dx= int_1^2frac3xx^3~dx -5 int_1^2frac1x^3~dx$$
$$=3int_1^2 x^-2 dx -5int_1^2 x^-3dx$$
You should take over from here and finish the problem.
answered Aug 30 at 1:34
Mohammad Riazi-Kermani
31k41853
add a comment |Â
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
accepted
Notice that
beginequation
frac3x - 5x^3
=
frac3xx^3
-
frac5x^3
=
frac3x^2
-
frac5x^3
=
3 x^-2 - 5x^-3
endequation
So the integration becomes
beginequation
3 int x^-2 - 5 int x^-3
=
3 fracx^-3-3
-
5
fracx^-4-4
endequation
Can you take it from here ?
answered Aug 30 at 1:32
Ahmad Bazzi
4,9001623
... Somehow I completely convinced myself that I didn't know how to integrate negative powers of $x$. Thanks!
– TheAssistant
Aug 30 at 1:34
1
@TheAssistant: Just remember an exponent of $-1$ needs to be handled differently.
– Clayton
Aug 30 at 1:46
add a comment |Â
up vote
2
down vote
accepted
Notice that
beginequation
frac3x - 5x^3
=
frac3xx^3
-
frac5x^3
=
frac3x^2
-
frac5x^3
=
3 x^-2 - 5x^-3
endequation
So the integration becomes
beginequation
3 int x^-2 - 5 int x^-3
=
3 fracx^-3-3
-
5
fracx^-4-4
endequation
Can you take it from here ?
answered Aug 30 at 1:32
Ahmad Bazzi
4,9001623
... Somehow I completely convinced myself that I didn't know how to integrate negative powers of $x$. Thanks!
– TheAssistant
Aug 30 at 1:34
1
@TheAssistant: Just remember an exponent of $-1$ needs to be handled differently.
– Clayton
Aug 30 at 1:46
add a comment |Â
up vote
2
down vote
accepted
up vote
2
down vote
accepted
Notice that
beginequation
frac3x - 5x^3
=
frac3xx^3
-
frac5x^3
=
frac3x^2
-
frac5x^3
=
3 x^-2 - 5x^-3
endequation
So the integration becomes
beginequation
3 int x^-2 - 5 int x^-3
=
3 fracx^-3-3
-
5
fracx^-4-4
endequation
Can you take it from here ?
answered Aug 30 at 1:32
Ahmad Bazzi
4,9001623
Notice that
beginequation
frac3x - 5x^3
=
frac3xx^3
-
frac5x^3
=
frac3x^2
-
frac5x^3
=
3 x^-2 - 5x^-3
endequation
So the integration becomes
beginequation
3 int x^-2 - 5 int x^-3
=
3 fracx^-3-3
-
5
fracx^-4-4
endequation
Can you take it from here ?
answered Aug 30 at 1:32
Ahmad Bazzi
4,9001623
answered Aug 30 at 1:32
Ahmad Bazzi
4,9001623
answered Aug 30 at 1:32
Ahmad Bazzi
4,9001623
answered Aug 30 at 1:32
Ahmad Bazzi
4,9001623
4,9001623
... Somehow I completely convinced myself that I didn't know how to integrate negative powers of $x$. Thanks!
– TheAssistant
Aug 30 at 1:34
1
@TheAssistant: Just remember an exponent of $-1$ needs to be handled differently.
– Clayton
Aug 30 at 1:46
add a comment |Â
... Somehow I completely convinced myself that I didn't know how to integrate negative powers of $x$. Thanks!
– TheAssistant
Aug 30 at 1:34
1
@TheAssistant: Just remember an exponent of $-1$ needs to be handled differently.
– Clayton
Aug 30 at 1:46
... Somehow I completely convinced myself that I didn't know how to integrate negative powers of $x$. Thanks!
– TheAssistant
Aug 30 at 1:34
... Somehow I completely convinced myself that I didn't know how to integrate negative powers of $x$. Thanks!
– TheAssistant
Aug 30 at 1:34
1
1
@TheAssistant: Just remember an exponent of $-1$ needs to be handled differently.
– Clayton
Aug 30 at 1:46
@TheAssistant: Just remember an exponent of $-1$ needs to be handled differently.
– Clayton
Aug 30 at 1:46
add a comment |Â
up vote
3
down vote
$$int_1^2frac3x-5x^3~dx= int_1^2frac3xx^3~dx -5 int_1^2frac1x^3~dx$$
$$=3int_1^2 x^-2 dx -5int_1^2 x^-3dx$$
You should take over from here and finish the problem.
answered Aug 30 at 1:34
Mohammad Riazi-Kermani
31k41853
add a comment |Â
up vote
3
down vote
$$int_1^2frac3x-5x^3~dx= int_1^2frac3xx^3~dx -5 int_1^2frac1x^3~dx$$
$$=3int_1^2 x^-2 dx -5int_1^2 x^-3dx$$
You should take over from here and finish the problem.
answered Aug 30 at 1:34
Mohammad Riazi-Kermani
31k41853
add a comment |Â
up vote
3
down vote
up vote
3
down vote
$$int_1^2frac3x-5x^3~dx= int_1^2frac3xx^3~dx -5 int_1^2frac1x^3~dx$$
$$=3int_1^2 x^-2 dx -5int_1^2 x^-3dx$$
You should take over from here and finish the problem.
answered Aug 30 at 1:34
Mohammad Riazi-Kermani
31k41853
$$int_1^2frac3x-5x^3~dx= int_1^2frac3xx^3~dx -5 int_1^2frac1x^3~dx$$
$$=3int_1^2 x^-2 dx -5int_1^2 x^-3dx$$
You should take over from here and finish the problem.
answered Aug 30 at 1:34
Mohammad Riazi-Kermani
31k41853
answered Aug 30 at 1:34
Mohammad Riazi-Kermani
31k41853
answered Aug 30 at 1:34
Mohammad Riazi-Kermani
31k41853
answered Aug 30 at 1:34
Mohammad Riazi-Kermani
31k41853
31k41853
add a comment |Â
add a comment |Â
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2
Split it and find integeration seperately
– Abhinav
Aug 30 at 1:31
1
While I admittedly made a rather simple mistake here, I'm curious to know where the downvotes are coming from. Is this question not up to quality standards here, outside of the actual math?
– TheAssistant
Aug 30 at 1:39
2
OP, I'm not sure what the downvotes are from. You've demonstrated effort (albeit a simple mistake). I say: Keep up the good work and ask questions as you need to...
– Clayton
Aug 30 at 1:44
Why do you guys downvote ? The OP has posted the question with his/her attempts. I'm not sure why the downvotes are for.
– Ahmad Bazzi
Aug 30 at 2:07