Home
Class 12
MATHS
Let I(n) = underset(0)overset(1//2)int(1...

Let `I_(n) = underset(0)overset(1//2)int(1)/(sqrt(1-x^(n))) dx` where `n gt 2`, then

A

`I_(n) lt pi/6`

B

`I_(n) gt pi/6`

C

`I_(n) gt 1pi2`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise Exercise 2 Part - IV|6 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise Exercise 3 Part - I|49 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise Exercise 2 Part - II|17 Videos

  • COMBINATORICS

    RESONANCE ENGLISH|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|5 Videos

  • DPP

    RESONANCE ENGLISH|Exercise QUESTION|656 Videos

Similar Questions

Explore conceptually related problems

int(sqrt(1+x^2)-x)^n dx

If I=underset (0)overset(1) int cos{ 2 "cot"^(-1)sqrt((1-x)/(1+x))}dx then

Evaluate the following definite integrals underset(0)overset(1)int(dx)/(sqrt(1-x^(2)))

If I=overset(1)underset(0)int (1)/(1+x^(pi//2))dx then

Show that (i) (1)/(10sqrt(2))lt underset(0)overset(1)int(x^(9))/(sqrt(1+x))dx lt 1/10 , (ii) 1/2 ln 2 lt int_(0)^(1)(tanx)/(1+x^(2))dx lt (pi)/(2)

int((a+bsin^(-1)x)^(n))/(sqrt(1-x^(2)))dx

The value of (.^(n)C_(0))/(n)+(.^(n)C_(1))/(n+1)+(.^(n)C_(2))/(n+2)+"..."+(.^(n)C_(n))/(2n) (a) underset(0)overset(1)intx^(n-1)(1+x)^(n)dx (b) underset(1)overset(2)intx^(n)(x-1)^(n-1)dx (c) underset(1)overset(2)int(1+x)^(n)dx (d) underset(0)overset(1)int(1-x)^(n)x^(n-1)dx

If I=int_(0)^(1//2) (1)/(sqrt(1-x^(2n)))dx then which one of the following is not true ?

If l=int_(0)^(1//2)(dx)/(sqrt(1-x^(2n))), n in N then (Where, [.] denotes G.I.F)

Let I_(n) = int_(0)^(1)x^(n)(tan^(1)x)dx, n in N , then

RESONANCE ENGLISH-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 2 Part - III
  1. Let a function f be even and integrable everywhere and periodic with p...

    Text Solution

    |

  2. Let f : R rarr R be defined as f(x) = int(-1)^(e^(x)) (dt)/(1+t^(2)) +...

    Text Solution

    |

  3. If a,b in R^(+) then find Lim(nrarroo) sum(k=1)^(n) ( n)/((k+an)(k+bn...

    Text Solution

    |

  4. Let f(x) = int(x)^(x+(pi)/(3))|sin theta|d theta(x in [0,pi])

    Text Solution

    |

  5. If f(x) in inegrable over [1,2] then int(1)^(2) f(x) dx is equal to :

    Text Solution

    |

  6. Let I(n) = underset(0)overset(1//2)int(1)/(sqrt(1-x^(n))) dx where n ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  19. A function f(x) satisfying int(0)^(1) f(tx)dt=n f(x), where xgt0, is

    Text Solution

    |

  20. Find the area bounded by y=sin^(-1)x ,y=cos^(-1)x ,and the X-axis.

    Text Solution

    |