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How to evaluate the definite integral from 0 to a [sin^-1[(x/a+x)^1/2]dx]

How to evaluate the definite integral from 0 to a [sin^-1[(x/a+x)^1/2]dx]

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Grade:12

1 Answers

vishal
38 Points
3 years ago
Let ... x=a tan ^2(t) Then. dx=2a tan(t)sec^2(t) dt & x= 0 to a...then. t=0 to π/4Put in the integral Then the integral from 0 to π/4 {sin^-1√[a tan^2(t)/a+atan^2(t)][2a tan(t) sec^2(t) dtAnd solve easily....And ans.. is ..2a

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