Find the area of the indicated region. We suggest you graph the curves to check whether one is above the other or whether they cross, and that you use technology to check your answer.

Question

Between y = −x and y = −x^3 for x in [−1, 1]

Answer 1

both odd functions through origin
same area both sides of y axis

2 times integral 0 to 1 of xdx - x^3dx
= 2(1^2/2 - 1^4/4) = 2(1/2-1/4) = 2(1/4)
=1/2