- #1

AdityaDev

- 527

- 33

## Homework Statement

$$\int_0^{\pi/2}(sinx-cosx)ln(sinx)dx$$

## Homework Equations

##int_0^af(x)dx=int_0^af(a-x)dx##

## The Attempt at a Solution

Using above equation, you get (without integral sign):

##(sinx-cosx)ln(tanx)## but it did not make any difference.

I got the answer by splitting the integral to ##sinxln(sinx)## and ##cosxln(cosx)## and then using integration by parts.(Answer verified without limits in wolfram alpha)

But the answer was long and time taking. Also the question is objective type and there has to be a shorter method. Can you provide a shorter method?