Home
Class 12
MATHS
Find the value of int(0)^(pi//2)sin2xlog...

Find the value of `int_(0)^(pi//2)sin2xlogtanxdx`.

Text Solution

Verified by Experts

The correct Answer is:
`0`
`I=int_(0)^(pi//2)sin2x log tan x dx`
`=int_(0)^(pi//2) sin2((pi)/2-x)"log tan"((pi)/2-x)dx`
`=-int_(0)^(pi//2)sin 2x log tan x dx=-1`
or `2I=0`
or `I=0`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 8.6|7 Videos

  • DEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 8.7|6 Videos

  • DEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 8.4|10 Videos

  • CURVE TRACING

    CENGAGE|Exercise Exercise|24 Videos

  • DETERMINANT

    CENGAGE|Exercise Multiple Correct Answer|5 Videos

Similar Questions

Explore conceptually related problems

The value of int_0^(pi/2)sin2x.log tanxdx is

int_(0)^(pi//2)sin^(2)xdx=?

(i) Show that int_(0)^(pi)xf(sinx)dx =(pi)/(2)int_(0)^(pi)f (sin x)dx. (ii) Find the value of int_(-1)^(3//2)|x sin pix|dx .

Find the value of int_(-pi/4)^( pi)sin^(2)xdx

Prove that int_0^(pi/2) sin2xlogtanxdx=0

evaluate int_(0)^((pi)/(3))sin2xdx

Evaluate : int_(0)^(pi//2) sin x dx

Find the value of int_(-1)^(2)|x sin pi x|dx