Home
Class 12
MATHS
Evaluate: int(-1)^1(x^3+|x|+1)/(x^2+2|x|...

Evaluate: `int_(-1)^1(x^3+|x|+1)/(x^2+2|x|+1)dx`

Text Solution

Verified by Experts

The correct Answer is:
`2log_(e)2`
`I=int_(-1)^(1)(x^(3)+|x|+1)/(x^(2)+2|x|+1)dx`
`=int_(-1)^(1)(x^(3))/(x^(2)+2|x|+1)dx+int_(-1)^(1)(|x|+1)/(x^(2)+2|x|+1)dx`
`=0+2int_(0)^(1)((|x|+1)/(|x|+1)^(2))dx=2int_(0)^(1)(dx)/(1+x)`
`=2In(1+x)|_(0)^(1)=2In2`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 8.8|7 Videos

  • DEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 8.9|9 Videos

  • DEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 8.6|7 Videos

  • CURVE TRACING

    CENGAGE|Exercise Exercise|24 Videos

  • DETERMINANT

    CENGAGE|Exercise Multiple Correct Answer|5 Videos

Similar Questions

Explore conceptually related problems

Evaluate int_(-1)^(1)(x^2-3x+2)dx

Evaluate : int_(1)^(2)(x^(3)-1)/(x^(2))dx

Evaluate int_(-1)^2 |x|/x dx

Evaluate int_(-3)^(2)|x-1|dx

Evaluate : int_(-1)^(1)(x^(2))/(1+x^(2))dx

Evaluate : int_(1)^(2) (x )/(1+x^(2))dx

Evaluate int_(-2)^(1)(|x|)/(x)dx

Evaluate int_(-2)^(1)(|x|)/(x)dx

Evaluate int_-1^1 x^3 (1-x^2)dx

Evaluate :int_(1)^(2)(x+3)/(x(x+2))dx