I have the double integral $$\iint (x^4+y^2)dxdy$$ for the bounded region $y=x^2$ and $y=x^3$
Is this simple as integrating with respect to x, followed by y with $x^3$ and $x^2$ as limits?
So i would have $$\int \frac{1}{5}x^5 + xy^2 dy=[\frac{1}{5}x^5y+\frac{1}{3}xy^3]$$
Then adding in the limits we get $$(\frac{1}{5}x^8+\frac{1}{3}x^{10})-(\frac{1}{5}x^7+\frac{1}{3}x^{7})$$
Is this the correct? Many thanks
If you are integrating in order $dydx$, your $y$ limits are from $x^{3}$ to $x^{2}$ and x limits are from 0 to 1 (these are points of intersection of two curves)
When integrating w.r.t order $dxdy$, you will have limits for $x=y^{1/3}$(since region is in first quadrant we take positive sign) to $x=y^{1/2}$ and $y$ limits are from $0$ to $1$