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\[\int\limits\limits_{-a}^{a} \sqrt{\frac{a-x}{a+x}}\]

Lets say, \( f(x)= \sqrt{\frac{a-x}{a+x}} \) , now f(X) is even or odd?

even or odd?

multiply and divide by the numerator

There is a property of definite integral which I think could be used here.

then the equation becomes solvable

hm letme see

hmm i think i know the answer, but not sure why it should be easy

let x=acosθ

can you post it ?

|dw:1326825738809:dw|

|dw:1326825797080:dw|

now you substitute x=acos O

answer is
\[a\pi\] but not sure why yet

well i don't think this beast is even or odd

would be odd without the radical

ahh, i think dhashni has it!

No sat after you break it as dash showed, the first is even and the second is odd.

ahh, and second integral is 0 for sure

so the first term reduces to zero.

hmm

i got zero for the second one, maybe i am wrong

how second? the first is even and the second is odd.

no i am right, second on is zero

if even, then
\[\int_{-a}^a f(x)dx=2\int_0^af(x)dx\]

Oh yes ... my apologies, yes the the second is zero.

For the first one we can use the step.

which is 0 and a and -a, so that one is gone.

So as the second one is odd and hence zero, we have to evaluate the first one.

sat, that's great :D

sorry, i meant the limits as x goes to a, not as x goes to zero

Lol OkaYy :D Thaanks a Lot :D