Home
Class 12
MATHS
"If " I=(dx)/(root(3)(sin^(11)xcosx))=-A...

"If " I=(dx)/(root(3)(sin^(11)xcosx))=-A(tanx)^(-(8)/(3))+B(tanx)^(-(2)/(3))+c," then the value of " 4A+B " is"-.`

Text Solution

Verified by Experts

The correct Answer is:
-3
`I=int(dx)/(sin^(11//3)x cos^(1//3)x)`
`=int(dx)/(tan^(11//3)x cos^(4)x)`
`=int((1+tan^(2)x)sec^(2)xdx)/(tan^(11//3)x)`
`=int((1+t^(2))dt)/(t^(11//3)) " " ("where " tanx=t)`
`=-(3)/(8)t^(-(8)/(3))-(3)/(2)t^(-(2)/(3))+c, " where " t=tanx`
` :. 4A+B=-3`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise JEE Main Previous Year|7 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise JEE Advanced Previous Year|1 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Matrix)|4 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(dx)/root3(sin^(11)xcosx)

If int(3tan(x-(pi)/(4)))/(cos^(2)xsqrt(tan^(3)x)+tan^(2)x+tanx)=Ktan^(-1)(sqrt(tanx+1+cotx))+C, then the value of K is

lim_(xto0)(tanx-sinx)/x^(3)

"I f"int(dx)/(cos^3xsqrt(sin2x))=a(tan^2x+b)sqrt(tanx)+c

If (sqrt(8)+i)^(50)=3^(49)(a+i b) , then find the value of a^2+b^2dot

int e^(x)((2 tanx)/(1+tanx)+cot^(2)(x+(pi)/(4)))dx is equal to

Provethat int_(0)^((pi)/(2))(dx)/(1+tanx)=(pi)/(4)

If det, (A-B) ne 0, A^(4)=B^(4), C^(3) A=C^(3)B and B^(3)A=A^(3)B , then find the value of det. (A^(3)+B^(3)+C^(3)) .

In a Delta ABC , if cosA cos B cos C= (sqrt3-1)/(8) and sin A sin B sin C= (3+ sqrt3)/(8) , then The value of tan A + tan B + tan C is

int_(0)^(pi)|cosx|^(3) dx is equal to (a) (4)/(3) (b) (2)/(3) (c) 0 (d) (-8)/(3)