Home
Class 12
MATHS
Evaluate: int(sinx)/(sin(x-a))dx...

Evaluate: `int(sinx)/(sin(x-a))dx`

Text Solution

Verified by Experts

The correct Answer is:
`(x-a)cosa+sin a log|sin(x-a)|+C`
`int(sinx)/(sin(x-a))dx=int(sin(x-a+a))/(sin(x-a)) dx`
`=int(sin(x-a)cosa+cos(x-a)sina)/(sin(x-a))dx`
`=cos a int dx+sin a int(cos(x-a))/(sin(x-a))dx`
`=(cosa)x+sina|log sin(x-a)|+C`
`=(x-a)cosa+sin a log|sin(x-a)|+C`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 7.4|20 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 7.5|9 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 7.2|7 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

Evaluate: int(sinx)/(sin4x)dx

Evaluate: int(sinx)/(2+sin2x)dx

Evaluate int(sinx)/(1+sinx)dx

Evaluate: int1/(sin(x-a)sin(x-b))dx

int(2sinx)/(3+sin2x)\ dx

Evaluate: int sin x/ (1+sinx) dx

Evaluate: int(x-sinx)/(1-cosx)dx

Find int(sinx)/(sin(x+1))dx

Evaluate: int(sinx)/(cos2x)\ dx

Evaluate: int(cotx)/(sqrt(sinx))dx