Question

integrate

Answer 1

\[\int\limits_{0}^{\pi}xdx \div(a^2-\cos^2x)\]

Answer 2

@ganeshie8

Answer 3

show that if \[U{n=\int\limits_{0}^{2a}}x^{n }\sqrt{2ax-x^2}dx,U{n}=((2n+1)\div(n+2))timesaU _{n-1}\]

Answer 4

put \[x=2asin^2\theta \]

Answer 5

@Ashleyisakitty

Answer 6

\[2ax-x^2=-(x^2-2ax)=-(x^2-2ax+a^2)+a^2 \\= -(x-a)^2+a^2=a^2-(x-a)^2\]

Answer 7

\[=a^2(1-(\frac{x-a}{a})^2)\]

Answer 8

so I think the sub would be be sin(theta)=(x-a)/a

Answer 9

and i think this is integration by parts for sure

Answer 10

we need to integrate that sqrt(2ax-x^2) part
and differentiate the x^n part

Answer 11

@freckles put x=2asin^2(theta)

Answer 12

is that required?

Answer 13

@freckles its not .thank u for answer

Answer 14

So that is the sub you came up with?

Answer 15

and maybe integration by parts won't work
just the first think that popped into my head

Answer 16

looks like you are asking two different questions. the first question is an integral

Answer 17

a definite integral involving cos