Question

Find the area of the indicated region:
Between y = x^2(x3 + 1)^10 and y = −x(x2 + 1)^10 for x in [0, 1]

Answer 1

\[\begin{vmatrix}\int_{0}^{1}(f(x)-g(x))\ dx\end{vmatrix}\]
where f(x) and g(x) are the given functions

Answer 2

you would also have to determine if there are any cross overs within the interval to be sure

Answer 3

x^2(x3 + 1)^10 = −x(x2 + 1)^10

x(x3 + 1)^10 = −(x2 + 1)^10

x= −[(x2 + 1)/(x3 + 1)] ^10

yeah, that does not look fun at all :)

Answer 4

well, the good news is that they dont intersect between 0 and 1 :)

http://www.wolframalpha.com/input/?i=x%5E2%28x3+%2B+1%29%5E10++%3D+%E2%88%92x%28x2+%2B+1%29%5E10