Reverse the order of integration?

Question

I'm not sure I follow the concept of reversing the integral. Why do I need to reverse it?
And how would I do that? For example, if I have the double integral of
∫(from 0 to 1) ∫(from sqrt(y) to 1) sqrt(2 + x^3) dxdy, what would the reverse integral be?

Answer 1

it's because you can't integrate sqrt(2 + x^3) with respect to x first. This is non-elementary integral.



you need to draw your region to see reverse process.

The region is the area under y = x^2, and x ranges from 0 to 1.



so ∫∫ sqrt(2 + x^3) dy dx, y = 0 to x^2, and x = 0 to 1.



integrate with respect to y first,

y sqrt(2 + x^3)



evaluating the limits

x^2 sqrt(2+x^3)



now integrate with respect to x

(2/9) (2+x^3)^(3/2)



evaluating the limits

(2/9) (3^(3/2) - 2^(3/2))



or

(2/9) (sqrt(27) - sqrt(8))

Answer 2

Whats your major lol lets be homework buddies ok.

Answer 3

confusing problem. lookup into google or bing. that could actually help!