Home
Class 12
MATHS
If int (3sin x+2 cosx)/(3cosx+2sinx)dx=a...

If `int (3sin x+2 cosx)/(3cosx+2sinx)dx=ax+blog_(e)|2 sinx+3 cosx|+c` then

A

`a= -(12)/(13)`

B

`b=(6)/(13)`

C

`a=(12)/(13)`

D

`b= -(15)/(39)`

Text Solution

Verified by Experts

The correct Answer is:
C, D
Differentiating both sides w.r.t. x, we get
`(3sin x+2 cosx)/(3cosx+2sinx)=a+(b(2cosx-3sinx))/((2sinx+3cosx))`
`=(sinx.(2a-3b)+cosx.(3a+2b))/((3cosx+2 sinx))`
Comparing like terms on both sides, we get
`3=2a-3b, 2=3a+2b`
`implies a=(12)/(13), b= -(15)/(39)`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Comprehension)|17 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Matrix)|4 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Single)|77 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(3sinx+2cosx)/(3cosx+2sinx)dx.

int (cosx)/(sqrt(2+sinx))dx

int(sinx)/((2+cosx)^(2))dx

Find int(cos2x)/((cosx+sinx)^(2))dx .

Evaluate: int((3sinx-2)cosx)/(5-cos^2x-4sinx)\ dx

Find int(cosx)/(sqrt(1+sinx))dx

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

int_(0)^(pi)(cosx)/(1+sinx)dx=

int((e^(x)+cosx))/(e^(x)+sinx+2)dx :

int _0^(pi/2) (sin^2x)/(sinx+cosx)dx