Home
Class 12
MATHS
Evaluate the following integrals: (1-...

Evaluate the following integrals: (1-35) `int_(-2)^2(3x^3+2|x|+1)/(x^2+|x|+1)dx`

Text Solution

Verified by Experts

We have `(2−3x)(3+2x)(1−2x)`
`=(2(3+2x)−3x(3+2x))(1−2x)`
` =(6+4x−9x−6x ^2 )(1−2x)`
`=(6−5x−6x ^ ...
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY

    RD SHARMA|Exercise Solved Examples And Exercises|277 Videos

  • DERIVATIVES AS A RATE MEASURER

    RD SHARMA|Exercise Solved Examples And Exercises|149 Videos

Similar Questions

Explore conceptually related problems

Evaluate the following integral: int_1^2|x-3|dx

Evaluate the following integrals: int_(-1)^(1)x^(3)|x|dx

Evaluate the following integral: int_(-1)^2|2x+3|dx

Evaluate the following integral: int_(-1)^1|2x+1|dx

Evaluate the following integral: int_(-2)^2|x+1|dx

Evaluate the following integral: int_1^2(3x)/(9x^2-1)dx

Evaluate the following integral: int_(1)^(3)|x^(2)-4|dx

Evaluate the following integrals: int_(-2)^(2) (dx)/(1+|x-1|)

Evaluate each of the following integral: int_(-2)^1(|x|)/x dx

Evaluate the following integrals: int(2-3x)(3+2x)(1-2x)dx

RD SHARMA-DEFINITE INTEGRALS-Solved Examples And Exercises
  1. Evaluate: int0^(pi//4)sqrt(1+sin2x)dx (ii) int0^(pi//4)sqrt(1-sin2x...

    Text Solution

    |

  2. Evaluate: int(pi//4)^(pi//2)sqrt(1-sin2x)dx

    Text Solution

    |

  3. Evaluate the following integrals: (1-35) int(-2)^2(3x^3+2|x|+1)/(x^...

    Text Solution

    |

  4. Evaluate the following integrals: (1-35) int0^pixsinx cos^2x dx

    Text Solution

    |

  5. Show that: int0^(pi//2)f(sin2x)sinxdx=sqrt(2)int0^(pi//4)f(cos2x)co...

    Text Solution

    |

  6. For x >0,l e tf(x)=int1^x((log)e t)/(1+t)dtdot Find the function...

    Text Solution

    |

  7. Evaluate the following integrals: (1-35) int0^(pi//2)(sin^n x)/(sin...

    Text Solution

    |

  8. Prove that: int0^(2pi)(xsin^(2n)x)/(sin^(2n)+cos^(2n)x)dx= pi^2

    Text Solution

    |

  9. Prove that: int0^(pi//2)log|tanx+cotx|dx=pi(log)e2

    Text Solution

    |

  10. Evaluate: int(-2)^2|xcospix|dx

    Text Solution

    |

  11. Evaluate: int(pi//4)^(pi//4)log(sinx+cosx)dx

    Text Solution

    |

  12. Evaluate: int0^pixlogsinxdx

    Text Solution

    |

  13. If int0^pi 1/(a+bcosx)dx=pi/sqrt(a^2-b^2), then int0^pi 1/(a+bcosx)^2d...

    Text Solution

    |

  14. int0^1sqrt((1-x)/(1+x))dx= (pi)/2 (b) (pi)/2-1 (c) (pi)/2+1 (d) ...

    Text Solution

    |

  15. int0^(pi//2)(cosx)/((2+sinx)(1+sinx))dx equals (a)log(2/3) (b) l...

    Text Solution

    |

  16. int0^pi(xtanx)/(secx+cosx)dxi s (pi^2)/4 (b) (pi^2)/2 (c) (3pi^2)/2...

    Text Solution

    |

  17. int0^2 1/(1+tanx)dx is equal to (pi^)/4 (b) (pi^)/3 (c) (pi^)/2 ...

    Text Solution

    |

  18. int(-pi//2)^(pi//2)"sin"|x|dx is equal to 1 (b) 2 (c) -1 (d) ...

    Text Solution

    |

  19. The value of the integral int0^oox/((1+x)(1+x^2))dx is (pi)/2 (b) ...

    Text Solution

    |

  20. int0^3(3x+1)/(x^2+9)dx = (pi)/(12)+log(2sqrt(2)) (b) (pi)/2+log(2sqr...

    Text Solution

    |