(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Evaluate the following repeated integral:

[tex] \int^2_0 dv \int^\frac{1}{2}_0 \frac{v}{\root(1-u^2) du} [/tex]

3. The attempt at a solution

since 1/something is something ^(-1), and root something is something^(1/2), i rearragned to get..

[tex] \int^2_0 dv \int^\frac{1}{2}_0 1 - u^2)^\frac{1}{2} du} [/tex]

integrating using standard integral

[tex] (ax+b)^n = \frac{(ax+b)^{n+1}}{a(n+1)} [/tex]

[tex] \int^2_0 [ \frac{(1 - u^2)^{1/2}}{-1(\frac{v}{2})} [/tex]

which i solved to get.

[tex]\int^2_0 -\frac{2(\frac{3}{4})^{3/4}}{v} dv

[/tex]

given that the answer in the book is pi over 3, i think i've made a mistake (also that 3/4 ^ 3/4 doesn't look right since surley it won't resolve well?)

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# Repeaded Integrals again

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