Double Integral: int int y sqrt(x^3 + 2) dx dy

[Daniel_Feldman]

I need to evaluate this integral. I'm pretty lousy with latex so bear with me.

The integrand is ysqrt(x^3+2)dxdy.

The limits on y are 0 to 1, and the limits for x are 5y to 5.

I tried switching the order of integration, so my limits became (1/5)x to 1, and 0 to 5 for x. However, when I tried to integrate, I end up getting something that could potentially be solved by parts, but I couldn't compute it. Can anyone help?

 

[pka]

\(\displaystyle \L \begin{array}{rcl}
\int\limits_0^1 {\int\limits_{5y}^5 {y\sqrt {x^3 + 2} dxdy} } & = & \int\limits_0^5 {\int\limits_0^{x/5} {y\sqrt {x^3 + 2} dydx} } \\
& = & \left. {\int\limits_0^5 {\frac{{y^2 }}{2}} \sqrt {x^3 + 2} dx} \right|_{y = 0}^{y = x/5} \\
& = & \int\limits_0^5 {\frac{{x^2 }}{{50}}} \sqrt {x^3 + 2} dx \\
\end{array} \\\)
Can you finish?

 

[Daniel_Feldman]

Yes, thanks.