- #1

Krushnaraj Pandya

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## Homework Statement

evaluate the following definite integral with limits 0 to 1## ∫log(sin(πx/2)) dx ##

2. The attempt at a solution

2. The attempt at a solution

I used ##∫f(x) = ∫f(a+b-x)## to get ## I=∫log(cos(πx/2))## with the same limits. Adding them and using ##log(m)+log(n)=log(mn)## and ##2sinxcosx=sin2x## I got ##2I=∫log(sin(πx)) - ∫log2## with same limits. The second part evaluates to ##log2##, I'm stuck on how to solve the first part. I'd appreciate some help, thank you. (Note-minimal use of indefinite integrals is to be done, this is supposed to be solved by properties of definite integrals such as mentioned in my attempt)