Home
Class 12
MATHS
I(1) = int(0)^(pi)(xsinx)/(1+cos^(2)x)d...

`I_(1) = int_(0)^(pi)(xsinx)/(1+cos^(2)x)dx, I_(2) = int_(0)^(pi)(x^(2)sinx)/((pi^(2)-3pix+3x^(2))(1+cos^(2)x))dx`, then

A

`I_(1) = (pi^(2))/(8)`

B

`I_(1) = (pi^(2))/(4)`

C

`I_(1) = I_(2)`

D

`I_(1) gt I_(2)`

Text Solution

Verified by Experts

The correct Answer is:
B, C
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise Exercise 2 Part - IV|9 Videos
  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise Exercise 3 Part - I|50 Videos
  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise Exercise 2 Part - II|23 Videos
  • COMBINATORICS

    RESONANCE|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|8 Videos
  • DPP

    RESONANCE|Exercise QUESTION|665 Videos

Similar Questions

Explore conceptually related problems

int_(0)^( pi)(sin x)/(1+cos^(2)x)dx =

int_(0)^(pi//2)(sinx)/((1+cos^(2)x))dx

int_(0)^( pi)(x)/(1+cos^(2)x)dx=

int_(0)^( pi/2)(sin x)/(1+cos x)dx

int_(0)^(pi//2)(dx)/((1+cos^(2)x))

int_0^(pi/2) (sinx)/(1+Cos^2x)dx

int_(0)^(pi//2) (dx)/(1+2 cos x)

Evaluate int_(0)^(pi)(xsinx)/((1+cos^(2)x))dx .

Evaluate: int_0^pi(xsinx)/(1+cos^2x)dx

RESONANCE-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 2 Part - III
  1. Let I(n) = int(0)^(1//2)(1)/(sqrt(1-x^(n))) dx where n gt 2, then

    Text Solution

    |

  2. If f(x) = 2^(|x|) where [x] denotes the fractional part of x. Then wh...

    Text Solution

    |

  3. Let f(x) = int(0)^(x)|2t-3|dt, then f is

    Text Solution

    |

  4. Let f(x) = int(0)^(pi)(sinx)^(n) dx, n in N then

    Text Solution

    |

  5. Let f(x) be a function satisfying f(x) f(x+2) = 10 AA x in R, then

    Text Solution

    |

  6. Let I(n) = int(0)^(pi)(sin^(2)(nx))/(sin^(2)x)dx, n in N then

    Text Solution

    |

  7. Let f(x) be a continuous function and I = int(1)^(9) sqrt(x)f(x) dx, t...

    Text Solution

    |

  8. Let A = int(1)^(e^(2))(lnx)/(sqrt(x))dx, then

    Text Solution

    |

  9. Let f(a,b) = int(a)^(b)(x^(2)-4x+3)dx, (bgt 0) then

    Text Solution

    |

  10. Let I = int(2)^(oo)((2x)/(x^(2)+1)- (1)/(2x+1)) dx & I is a finite r...

    Text Solution

    |

  11. Let f(x) is a quadratic expression with positive integral coefficient...

    Text Solution

    |

  12. I(1) = int(0)^(pi)(xsinx)/(1+cos^(2)x)dx, I(2) = int(0)^(pi)(x^(2)sin...

    Text Solution

    |

  13. Let L(1) = lim(xrarr0^(+)) (int(0)^(x^(2)) sinsqrt(t)dt)/(x-sinx), the...

    Text Solution

    |

  14. lim(nrarroo) ((1^(k)+2^(k)+3^(k)+"......"n^(k)))/((1^(2)+2^(2)+"....."...

    Text Solution

    |

  15. Let T(n) = sum(r=1)^(n) (n)/(r^(2)-2r.n+2n^(2)), S(n) = sum(r=0)^(n)(n...

    Text Solution

    |

  16. A function satisfying int0^1f(tx)dt=nf(x), where x>0 is

    Text Solution

    |

  17. Find the area bounded by y=sin^(-1)x ,y=cos^(-1)x ,a n dt h ex-a xi sd...

    Text Solution

    |

  18. Let f(x) be a non-negative, continuous and even function such that are...

    Text Solution

    |

  19. Let 'c' be a positive real number such that area bounded by y = 0 , y...

    Text Solution

    |

  20. Area bounded by y = x^(2)- 2|x| and y = -1 is equal to

    Text Solution

    |