Home
Class 12
MATHS
The value of the definite integral int(2...

The value of the definite integral `int_(2pi)^(5pi//2)(sin^(-1)(cosx)+cos^(-1)(sinx))dx` is equal to

A

`pi^2/8`

B

`pi^2/4`

C

`pi^2/2`

D

`pi^2`

Text Solution

Verified by Experts

The correct Answer is:
B
`:. sin^(-1) (cos x ) + cos^(-1) (sinx)` is periodic with period `2pi`, then
`int_(2pi)^(5pi//2) (sin^(-1) (cosx) + cos^(-1)(sinx))dx`
`=int_(0)^(pi//2) (sin^(-1) {cos(pi/2-2)} + cos^(-1){sin(pi/2-x)})dx`
`=int_(0)^(pi//2) (sin^(-1)sinx + cos^(-1)cosx)dx`
`=2int_0^(pi//2) xdx = 2{x^2/2}_0^(pi/2) =pi^2/4`
Promotional Banner

Topper's Solved these Questions

  • MOCK TEST 4

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION 2)|5 Videos

  • MOCK TEST 3

    VMC MODULES ENGLISH|Exercise PART III : MATHEMATICS (SECTION-2)|10 Videos

  • MOCK TEST 5

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION 2)|5 Videos

Similar Questions

Explore conceptually related problems

The value of the definite integral int_(t+2pi)^(t+5pi//2) {sin^(-1)(cosx)+cos^(-1)(cosx)} dx is equal to

Given int_(0)^(pi//2)(dx)/(1+sinx+cosx)=A . Then the value of the definite integral int_(0)^(pi//2)(sinx)/(1+sinx+cosx)dx is equal to

The value of the definite integral, int_0^(pi/2) (sin5x)/sinx dx is

Evaluate the definite integrals int_0^(pi/2)sin2xtan^(-1)(sinx)dx

The value of the definite integral int_(0)^(2npi) max (sinx,sin^(-1)( sinx)) dx equals to (where, n in l)

Evaluate the definite integrals int_(pi/6)^(pi/3)(sinx+cosx)/(sqrt(sin2x))dx

Evaluate the definite integrals int_(0)^(pi//4)(sinx+cosx)/(25-16(sinx-cosx)^(2)) dx

The value of the integral int_(-pi//3)^(pi//3) (x sinx)/(cos^(2)x)dx , is

The value of the integral int_(-pi/2)^(pi//2) sqrt((1+cos2x)/(2))dx is

Evaluate the definite integrals int_0^(pi)(sin^2(x/2)-cos^2(x/2))dx