Find the area of the indicated region. Enclosed by y = −x and y = x4

Answer 1

intersection:
x^4 = -x
x^4 + x = 0
x(x^3 +1) = 0
x(x+1)(x^2 -x + 1)= 0
2 real solutions,
x = 0 or x = -1
http://www.wolframalpha.com/input/?i=plot+y+%3D+x%5E4+%2C+y+%3D+-x

area = ∫(-x - x^4) from -1 to 0
= [- x^2/2 - x^5/5] form -1 to 0
= (0 - (-1 -(-1)/5)
= 1 - 1/5
= 4/5