Home
Class 12
MATHS
Let g(x)=int(1+2cosx)/((cosx+2)^2)dxa n ...

Let `g(x)=int(1+2cosx)/((cosx+2)^2)dxa n dg(0)=0.` then the value of `8g(pi/2)` is __________

Text Solution

Verified by Experts

The correct Answer is:
0.5
`g(x)=int(cosx(cosx+2)+sin^(2)x)/((cosx+2)^(2))dx`
`=int underset(II)(underbrace(cosx))*(1)/(underset(I)(underbrace((cosx+2))))dx+int(sin^(2)x)/((cosx+2)^(2))dx`
`=(1)/(cosx+2)*sinx-int(sin^(2)x)/((cosx+2)^(2))dx+int(sin^(2))/((cosx+2)^(2))dx`
`:. g(x)=(sinx)/(cosx+2)+C`
`g(0)=0 " or " C=0`
`:. g(x)=(sinx)/(cosx+2) " or " g((pi)/(2))=(1)/(2)`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise Archives JEE MAIN (Single Correct Answer Type)|7 Videos

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise Archives JEE ADVANCED (Single Correct Answer Type)|1 Videos

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise EXERCISES (Matrix Match Type)|4 Videos

  • HYPERBOLA

    CENGAGE PUBLICATION|Exercise COMPREHENSION TYPE|2 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE PUBLICATION|Exercise Single correct Answer|21 Videos

Similar Questions

Explore conceptually related problems

If M=int_0^((pi)/(2))(cosx)/(x+2)dx,N=int_0^((pi)/(4))(sinxcosx)/((x+1)^2)dx , then the value of M-N is

Let f(x)=int_2^x(dt)/(sqrt(1+t^4))a n dg(x) be the inverse of f(x) . Then the value of g'(0)

Evaluate int_0^(pi/2)(cosx)/(1+sinx)^2dx

If int(sinx^8-cosx^8)/(1-2sinx^2cosx^2)dx= asin2x +c , then find the value of a.

Let g(x) be differentiable on R and int_(sint)^1x^2g(x)dx=(1-sint), where t in (0,pi/2)dot Then the value of g(1/(sqrt(2))) is____

Let f(x)=sin x+cosx and g(x)=x^(2)-1 , then g{f(x)} is invertible if -

If I=int_0^((3pi)/4)[(1+x)sinx+(1-x)cosx]dx , then value of (sqrt(2)-1)I is_____

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

Iff(x)=e^(g(x))a n dg(x)=int_2^x(tdt)/(1+t^4), then find the value of f^(prime)(2)

The value of int_(0)^(pi)|cosx|dx is