Home
Class 12
MATHS
Evaluate the definite integralsint(pi/6...

Evaluate the definite integrals`int_(pi/6)^(pi/4) cose cxdx`

Text Solution

Verified by Experts

`I=int_(pi/6)^(pi/4) cosecx dx`
`=[log(cosecx-cotx]_(pi/6)^(pi/4)`
`=log(cosec(pi/4)-cot(pi/4))-log(cosec(pi/6)-cot(pi/6))`
`=log(sqrt2-1)-log(2-sqrt3)`
`=log{(sqrt2-1)/(2-sqrt3)}`
Promotional Banner

Topper's Solved these Questions

  • INTEGRALS

    NCERT ENGLISH|Exercise EXERCISE 7.6|24 Videos

  • INTEGRALS

    NCERT ENGLISH|Exercise EXERCISE 7.10|10 Videos

  • DIFFERENTIAL EQUATIONS

    NCERT ENGLISH|Exercise EXERCISE 9.1|12 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    NCERT ENGLISH|Exercise Solved Examples|13 Videos

Similar Questions

Explore conceptually related problems

Evaluate the definite integrals int_0^(pi/2) cos2xdx

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

Evaluate the definite integrals int0pi/4sin2xdx

Evaluate the definite integrals int_0^(pi/4)(tanx)dx

Evaluate the definite integrals int_0^(pi/2)cos^2xdx

Evaluate the definite integrals int_(4)^(5)e^xdx

Evaluate the definite integrals int_(0)^((pi)/(4)tan x)dx

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

Evaluate the following definite integral: int_(pi//6)^(pi//4)cos e c\ x\ dx

Evaluate the definite integral int_(pi/2)^(pi) e^x[(1-sin x)/(1-cos x)] dx