Home
Class 12
MATHS
int0^(pi//2)(sqrttanx+sqrtcotx)dx...

`int_0^(pi//2)(sqrttanx+sqrtcotx)dx`

Text Solution

Verified by Experts

`int_0^(pi/2)(sqrttanx+sqrtcotx)dx`
=`int_0^(pi/2)(sinx+cosx)/sqrt(sinxcosx)dx`
=`sqrt2int_0^(pi/2)(sinx+cosx)/sqrt(1-(sinx-cosx)^2)dx`
=`sqrt2[sin^-1(sinx-cosx)]_0^(pi/2)`
=`sqrt2(sin^-1 1-sin^-1(-1))`
=`sqrt2(pi/2+pi/2)=sqrt2pi`
Promotional Banner

Topper's Solved these Questions

  • Elements of Mathematics

    MBD PUBLICATION|Exercise QUESTION BANK|48 Videos

  • INTRODUCTION TO THREE DIMENSIONAL GEOMETRY

    MBD PUBLICATION|Exercise QUESTION BANK|40 Videos

Similar Questions

Explore conceptually related problems

int(sqrttanx+sqrtcotx)dx

Integrate: int_0^(pi/2)(sqrttanx)/(sqrttanx+sqrtcotx)dx

int_0^(pi/2)1/(1+tanx)dx

Write the value of int_(0)^(pi//2)(sinx)/(sinx+cosx)dx

int_0^(pi/2)In(tanx+cotx)dx

Evaluate int_0^(pi/2)(sqrt(sinx))/(sqrt(sinx)+sqrt(cos x))dx

Evaluate the following integrals int_0^(pi/2)(cosx-sinx)dx

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