Area enclosed by two curves.

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Find the area enclosed by two curves.



$y=x^2$ and $y=-x^2+x+1$



My answer:



$frac-12 le x le 1$



$x^2 le y le -x^2+x+1$



$int_^ int_^dxdy = int_- frac12 ^1 ( int_x^2^-x^2+x+1dy)dx$



$P= int_ frac-12 ^1left( (-x^2+x+1)-(x^2)right)= frac98$



Is that correct, because the answer in my excercice book is $frac sqrt5 6$




integration area curves




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  • I got the same as you, you I'd say the book is wrong, you are right...probably.
    – DonAntonio
    Jan 11 '17 at 22:07










  • How about that one: Find the volume of the solid enclosed by : $z=7-x^2$, $z=-2$, $y=-1$, $y=4$. My answer is 180, the answer in the book is again totally different..
    – M.Szostu
    Jan 11 '17 at 22:12










  • Yep, I get the same $;180;$ : $$int_-3^3int_-1^4int_-2^7-x^2dzdydx=180$$ Are you sure you're looking at the solutions in the correct chapter, sections...*book* ?
    – DonAntonio
    Jan 11 '17 at 22:31










  • I am, I checked multiple times to be sure, to be precise it is not a book per se, these are the materials our lecturer prepared for us, attaching allegedly "correct" answers. Ugh.
    – M.Szostu
    Jan 11 '17 at 22:33










  • Well, those notes at least will make a nice bonfire...:)
    – DonAntonio
    Jan 11 '17 at 22:34














up vote
1
down vote

favorite












Find the area enclosed by two curves.



$y=x^2$ and $y=-x^2+x+1$



My answer:



$frac-12 le x le 1$



$x^2 le y le -x^2+x+1$



$int_^ int_^dxdy = int_- frac12 ^1 ( int_x^2^-x^2+x+1dy)dx$



$P= int_ frac-12 ^1left( (-x^2+x+1)-(x^2)right)= frac98$



Is that correct, because the answer in my excercice book is $frac sqrt5 6$




integration area curves




share|cite|improve this question






















  • I got the same as you, you I'd say the book is wrong, you are right...probably.
    – DonAntonio
    Jan 11 '17 at 22:07










  • How about that one: Find the volume of the solid enclosed by : $z=7-x^2$, $z=-2$, $y=-1$, $y=4$. My answer is 180, the answer in the book is again totally different..
    – M.Szostu
    Jan 11 '17 at 22:12










  • Yep, I get the same $;180;$ : $$int_-3^3int_-1^4int_-2^7-x^2dzdydx=180$$ Are you sure you're looking at the solutions in the correct chapter, sections...*book* ?
    – DonAntonio
    Jan 11 '17 at 22:31










  • I am, I checked multiple times to be sure, to be precise it is not a book per se, these are the materials our lecturer prepared for us, attaching allegedly "correct" answers. Ugh.
    – M.Szostu
    Jan 11 '17 at 22:33










  • Well, those notes at least will make a nice bonfire...:)
    – DonAntonio
    Jan 11 '17 at 22:34












up vote
1
down vote

favorite









up vote
1
down vote

favorite











Find the area enclosed by two curves.



$y=x^2$ and $y=-x^2+x+1$



My answer:



$frac-12 le x le 1$



$x^2 le y le -x^2+x+1$



$int_^ int_^dxdy = int_- frac12 ^1 ( int_x^2^-x^2+x+1dy)dx$



$P= int_ frac-12 ^1left( (-x^2+x+1)-(x^2)right)= frac98$



Is that correct, because the answer in my excercice book is $frac sqrt5 6$




integration area curves




share|cite|improve this question














Find the area enclosed by two curves.



$y=x^2$ and $y=-x^2+x+1$



My answer:



$frac-12 le x le 1$



$x^2 le y le -x^2+x+1$



$int_^ int_^dxdy = int_- frac12 ^1 ( int_x^2^-x^2+x+1dy)dx$



$P= int_ frac-12 ^1left( (-x^2+x+1)-(x^2)right)= frac98$



Is that correct, because the answer in my excercice book is $frac sqrt5 6$





integration area curves





share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Aug 23 at 3:28









HugoTeixeira

22129




22129










asked Jan 11 '17 at 22:02









M.Szostu

192




192











  • I got the same as you, you I'd say the book is wrong, you are right...probably.
    – DonAntonio
    Jan 11 '17 at 22:07










  • How about that one: Find the volume of the solid enclosed by : $z=7-x^2$, $z=-2$, $y=-1$, $y=4$. My answer is 180, the answer in the book is again totally different..
    – M.Szostu
    Jan 11 '17 at 22:12










  • Yep, I get the same $;180;$ : $$int_-3^3int_-1^4int_-2^7-x^2dzdydx=180$$ Are you sure you're looking at the solutions in the correct chapter, sections...*book* ?
    – DonAntonio
    Jan 11 '17 at 22:31










  • I am, I checked multiple times to be sure, to be precise it is not a book per se, these are the materials our lecturer prepared for us, attaching allegedly "correct" answers. Ugh.
    – M.Szostu
    Jan 11 '17 at 22:33










  • Well, those notes at least will make a nice bonfire...:)
    – DonAntonio
    Jan 11 '17 at 22:34
















  • I got the same as you, you I'd say the book is wrong, you are right...probably.
    – DonAntonio
    Jan 11 '17 at 22:07










  • How about that one: Find the volume of the solid enclosed by : $z=7-x^2$, $z=-2$, $y=-1$, $y=4$. My answer is 180, the answer in the book is again totally different..
    – M.Szostu
    Jan 11 '17 at 22:12










  • Yep, I get the same $;180;$ : $$int_-3^3int_-1^4int_-2^7-x^2dzdydx=180$$ Are you sure you're looking at the solutions in the correct chapter, sections...*book* ?
    – DonAntonio
    Jan 11 '17 at 22:31










  • I am, I checked multiple times to be sure, to be precise it is not a book per se, these are the materials our lecturer prepared for us, attaching allegedly "correct" answers. Ugh.
    – M.Szostu
    Jan 11 '17 at 22:33










  • Well, those notes at least will make a nice bonfire...:)
    – DonAntonio
    Jan 11 '17 at 22:34















I got the same as you, you I'd say the book is wrong, you are right...probably.
– DonAntonio
Jan 11 '17 at 22:07




I got the same as you, you I'd say the book is wrong, you are right...probably.
– DonAntonio
Jan 11 '17 at 22:07












How about that one: Find the volume of the solid enclosed by : $z=7-x^2$, $z=-2$, $y=-1$, $y=4$. My answer is 180, the answer in the book is again totally different..
– M.Szostu
Jan 11 '17 at 22:12




How about that one: Find the volume of the solid enclosed by : $z=7-x^2$, $z=-2$, $y=-1$, $y=4$. My answer is 180, the answer in the book is again totally different..
– M.Szostu
Jan 11 '17 at 22:12












Yep, I get the same $;180;$ : $$int_-3^3int_-1^4int_-2^7-x^2dzdydx=180$$ Are you sure you're looking at the solutions in the correct chapter, sections...*book* ?
– DonAntonio
Jan 11 '17 at 22:31




Yep, I get the same $;180;$ : $$int_-3^3int_-1^4int_-2^7-x^2dzdydx=180$$ Are you sure you're looking at the solutions in the correct chapter, sections...*book* ?
– DonAntonio
Jan 11 '17 at 22:31












I am, I checked multiple times to be sure, to be precise it is not a book per se, these are the materials our lecturer prepared for us, attaching allegedly "correct" answers. Ugh.
– M.Szostu
Jan 11 '17 at 22:33




I am, I checked multiple times to be sure, to be precise it is not a book per se, these are the materials our lecturer prepared for us, attaching allegedly "correct" answers. Ugh.
– M.Szostu
Jan 11 '17 at 22:33












Well, those notes at least will make a nice bonfire...:)
– DonAntonio
Jan 11 '17 at 22:34




Well, those notes at least will make a nice bonfire...:)
– DonAntonio
Jan 11 '17 at 22:34















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