Home
Class 12
MATHS
int(sinx)/(sin(x-(pi)/(4)))dx " is equal...

`int(sinx)/(sin(x-(pi)/(4)))dx " is equal to "`

A

`(1)/(sqrt(2))(x+log_(e)|cos(x-(pi)/(4))|)+c`

B

`(1)/(sqrt(2))(x-log_(e)|sin(x-(pi)/(4))|)+c`

C

`sqrt(2)(x+log_(e)|sin(x-(pi)/(4))|)+c`

D

`(1)/(sqrt(2))(x+log_(e)|sin(x-(pi)/(4))|)+c`

Text Solution

Verified by Experts

The correct Answer is:
D
` int(sinx)/(sin(x-pi//4))dx=int(sin((x-(pi)/(4))+(pi)/(4)))/(sin(x-(pi)/(4)))dx`
`=(1)/(sqrt(2))int(sin(x-(pi)/(4))+cos(x-(pi)/(4)))/(sin(x-(pi)/(4)))dx`
`=(1)/(sqrt(2))int(1+cot sin(x-(pi)/(4)))dx`
`=(1)/(sqrt(2))(x+log_(e)|sin(x-(pi)/(4))|)+c`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Multiple)|17 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Comprehension)|17 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 7.9|15 Videos

  • HYPERBOLA

    CENGAGE|Exercise JEE Advanced Previous Year|14 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE|Exercise Single correct Answer|21 Videos

Similar Questions

Explore conceptually related problems

The value of sqrt(2)int(sinx)/(sin(x-(pi)/(4)))dx , is

int(sin(x-a))/(sinx)dx

int_(0)^( pi)(sin nx)/(sin x)dx is equal to

If int(sinx)/(sin(x-(pi)/(4)))dx=Af(x)+(1)/(sqrt2)log[|sinx-cosx|]+c, then

int(cosx-sinx)/(1+2sin x cosx)dx is equal to

The value of int(sinx-cosx)/(sqrt(sin2x)dx is equal to

int_0^(2pi) sin^5 (x/4) dx is equal to

The value of the int(sinx+cosx)/(3+sin2x)dx is equal to