Ex 7.11, 10 - Chapter 7 Class 12 Integrals

Transcript

Ex 7.11, 10 By using the properties of definite integrals, evaluate the integrals : 0 2 2 log sin log sin 2 Let I1= 0 2 2 log sin log sin 2 I1= 0 2 2 log sin 2 sin cos I1= 0 2 2 log sin log 2 log sin log cos I1= 0 2 log sin 2 log cos I1= 0 2 log sin 0 2 log 2 0 2 log cos Solving I2 I2= 0 2 log cos I2= 0 2 log 2 I2= 0 2 log sin Put the value of I2 in (1) i.e. I1 I1= 0 2 log sin 0 2 log 2 0 2 log cos I1= 0 2 log sin 0 2 log 2 0 2 log sin I1= 0 2 log 2 I1= log 2 0 2 I1= log 2 0 2 I1= log 2 2 0 I1= log 2 1 2 I1= 2 log 1 2