can someone help me solve it?
(integral from 0 to 4) dx (integral form x/2 to x^1/2) dy (x^2 - y^1/2)=
I ended up with:
(76/56) - (64*2^1/2)/21 + 64/(15*2^1/2)
help!!!
Hello, well, not so difficult, is integrated first with respect to $\displaystyle y$, we can separate into several integrals as follows:
$\displaystyle \displaystyle\int_{x/2}^{x^{1/2}} x^2.dy - \displaystyle\int_{x/2}^{x^{1/2}}y^{1/2}.dy $=
$\displaystyle x^2y\bigr]_{x/2}^{x^{1/2}} - \displaystyle\frac{2}{3} .y^{3/2}\bigr]_{x/2}^{x^{1/2}}$.
Evaluating......
$\displaystyle x^2( \sqrt[ ]{x} - \displaystyle\frac{x}{2} ) - (- \displaystyle\frac{1}{6} \sqrt[ ]{2} x^{3/2} + \displaystyle\frac{2}{3} x^{3/4}).
$
Simplify the latter expression, and the integrity of zero to four.
Greetings