Home
Class 12
MATHS
Evaluate: int0^(pi//2)(2logsinx-logsin2x...

Evaluate: `int_0^(pi//2)(2logsinx-logsin2x)dx`

Text Solution

Verified by Experts

Let,I=`int_0^(pi//2)(2logsinx-logsin2x)dx`
we have `f(x)=2logsinx−logsin2x`
`f(x)=log(sin^2x/sin2x)`
​ `=logtanx−log2`
I=`int_0^(pi//2)logtanx dx`
Let `y=π/2​−x,dy=−dx,tanx=coty`
...
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY

    RD SHARMA|Exercise Solved Examples And Exercises|277 Videos

  • DERIVATIVES AS A RATE MEASURER

    RD SHARMA|Exercise Solved Examples And Exercises|149 Videos

Similar Questions

Explore conceptually related problems

int_(0)^(pi//2) (2logsin x - log sin 2x) dx=

Prove that int_(0)^(pi//2)(2logsinx-logsin2x)dx=(pi)/(2)(log2) .

Evaluate: int_0^(pi//2)logtanx\ dx

Evaluate: int_0^(pi//2)cos^2x\ dx

Evaluate : int_0^(pi/2) x sinx dx

Evaluate: int_0^(pi//2)x/(sinx+cosx)dx

Evaluate of each of the following integral: int_0^(pi//2)(2logcos x-logs in\ 2x)dx

Evaluate int_0^(pi/2) xcosx dx

Evaluate: int_0^(pi//2)1/(4sin^2x+5cos^2x)dx

Evaluate: int_0^(pi//2)(s in x)/(1+cos^2x)dx