Question

integration 0-Π\2 x÷sinx+cosx

Answer 1

I hope this answer will helps you.Is it clear

Answer 2

Hi Mate!!!

We know that integration from a to b F ( x ) = integration from a to bF ( a + b - x )

I = Integration from 0 to π / 2 x / sin ( x ) + cos ( x ) ..... equation 1

I = Integration from 0 to π / 2 ( π / 2 - x ) / sin ( π / 2 -x ) + cos ( π / 2 - x )...... equation 2

Adding both the equations.

2I=Integration from 0 to π / 2 { π / 2 / sin ( x ) + cos ( x ) }

We also know that

sin ( x ) + cos ( x ) = √ 2 ( sin ( π / 4 + x ))

2I = Integration from 0 to π / 2√2 { Cosec ( π / 4 + x }

2I = π / 2√ 2 { Log ( Cosec ( π / 4 +x ) - cot ( π / 4 + x}. limits from 0 to π / 2.

I= π / 2 √2 log ( 3 + 2√2)

! nHope it helps!!!