Question

Integrate:

Answer 1

\[\int\limits_{d}^{0}\frac{\sqrt{x}}{\sqrt{d-x}}dx\]

Answer 2

the limits cant be right...function is undefined for x<0

Answer 3

good call

Answer 4

d>0

Answer 5

domain is 0<x<d

Answer 6

i do not think anything is wrong. The book says to substitute x=u\(^{2}\).

Answer 7

ok then

dx = 2u du

\[2 \int\limits \frac{\sqrt{u^{2}}*u}{\sqrt{d-u^{2}}} du\]

Answer 8

then make sub ...
u = sqrt(d)*sin w

du = sqrt(d)*cos w dw
\[2\int\limits \frac{d \sin^{2} w}{\sqrt{d} \sqrt{1-\sin^{2} w}}\sqrt{d} \cos w dw\]

Answer 9

\[=2d \int\limits \sin^{2} w dw\]

Answer 10

do you know integral of sin^2 ?

Answer 11

i think i got it. Thanks!

Answer 12

yw

Answer 13

Got the answer! Thanks again.