Pls Help me understand how this integral is solved?
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definite integral form 0 to 1 from sqrt(x) / ( sqrt(x)+sqrt(1-x) ) * sin (pi*x) .
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Answer:
There is a trick coz you can't possibly find an antiderivative for your expression. Set y = 1 - x. Using sin pi*x = sin (pi - pi*x) you see that your integral I is equal to definite integral form 0 to 1 of sqrt(1 -x) / ( sqrt(x)+sqrt(1-x) ) * sin (pi*x) dx where y has been changed back to x. Adding the 2 expressions, it follows that I + I = definite integral form 0 to 1 of 2 sin (pi*x) dx = 4/pi. So I = 2/pi.
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