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#### Petrus

##### Well-known member

- Feb 21, 2013

- 739

Hello MHB,

I got stuck on one exercise,

\(\displaystyle \int_0^1\int_y^{e^y}\sqrt{x}dxdy\)

So I antiderivate respect to x and get

\(\displaystyle \Bigl[\frac{2x^{\frac{3}{2}}}{3} \Bigr]_y^{e^y}\)

so we got:

\(\displaystyle \int_0^1\frac{2e^{\frac{2y}{3}}-2y^{\frac{2}{3}}}{3}\)

So I did try antiderivate that but as soon as I try antiderivate \(\displaystyle 2e^{\frac{2y}{3}}\) I would get \(\displaystyle \frac{2e^{\frac{6y}{3}}}{y}\) and we got zero in our limit that means I done something wrong and I cant see what I done wrong

edit: in the limits it's \(\displaystyle e^y\) it does not look clearly

Regards,

I got stuck on one exercise,

\(\displaystyle \int_0^1\int_y^{e^y}\sqrt{x}dxdy\)

So I antiderivate respect to x and get

\(\displaystyle \Bigl[\frac{2x^{\frac{3}{2}}}{3} \Bigr]_y^{e^y}\)

so we got:

\(\displaystyle \int_0^1\frac{2e^{\frac{2y}{3}}-2y^{\frac{2}{3}}}{3}\)

So I did try antiderivate that but as soon as I try antiderivate \(\displaystyle 2e^{\frac{2y}{3}}\) I would get \(\displaystyle \frac{2e^{\frac{6y}{3}}}{y}\) and we got zero in our limit that means I done something wrong and I cant see what I done wrong

edit: in the limits it's \(\displaystyle e^y\) it does not look clearly

Regards,

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