Home
Class 12
MATHS
If g(x)=int(sinx)^("sin"(2x))sin^(-1)(t)...

If `g(x)=int_(sinx)^("sin"(2x))sin^(-1)(t)dt ,t h e n :`
(a) `g^(prime)(pi/2)=-2pi` (b) `g^(prime)(-pi/2)=-2pi` (c) `g^(prime)(-pi/2)=2pi` (d) `g^(prime)(pi/2)=2pi`

A

`g'(-(pi)/(2)) = 2pi`

B

`g'(-(pi)/(2)) = - 2pi`

C

`g'((pi)/(2)) = 2pi`

D

`g'((pi)/(2)) = -2pi`

Text Solution

Verified by Experts

The correct Answer is:
BOUNS
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise Exercise 3 Part - II|25 Videos
  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise High Level Problem|26 Videos
  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise Exercise 2 Part - IV|6 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

Let F(x)=int_(sinx)^(cosx)e^((1+sin^(-1)(t))dt on [0,(pi)/(2)] , then

If g(x)=int_(0)^(x)cos^(4)t dt , then prove that g(x+pi)=g(x)+g(pi) .

If f(x)=|cosx-sinx| , find f^(prime)(pi/6) and f^(prime)(pi/3) .

If f(x)=|cosx-sinx| ,find f^(prime)(pi/6) and f^(prime)(pi/3)dot

If f(x)=int_0^x("cos"(sint)+"cos"(cost)dt ,t h e nf(x+pi)i s (a) f(x)+f(pi) (b) f(x)+2(pi) (c) f(x)+f(pi/2) (d) f(x)+2f(pi/2)

If g(x)=int_(0)^(x)cos^(4)t dt, then g(x+pi) equals to (a) (g(x))/(g(pi)) (b) g(x)+g(pi) (c) g(x)-g(pi) (d) g(x).g(pi)

f(x)=sinx+int_(-pi//2)^(pi//2)(sinx+tcosx)f(t)dt The range of f(x) is

int_(-pi/2)^(pi/2) |sin x| dx

If f(x)=sin^(-1)cosx , then the value of f(10)+f^(prime)(10) is (a) 11-(pi)/2 (b) (pi)/2-11 (c) (5pi)/2-11 (d) none of these

Evaluate: int_(-pi/2)^(2pi)sin^(-1)(sinx)dx

RESONANCE ENGLISH-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 3 Part - I
  1. Let f: RvecR be a function defined by f(x)={[x],(xlt=2) \ \ (0,x >2) ...

    Text Solution

    |

  2. If alpha=int0^1(e^(9x+3tan^(-1)x))((12+9x^2)/(1+x^2))dx where tan^(-1)...

    Text Solution

    |

  3. Let f: R rarr R be a continuous odd function, which vanishes exactly a...

    Text Solution

    |

  4. Let f(x)=7tan^8x+7tan^6x-3tan^4x-3tan^2x for all x in (-pi/2,pi/2) . ...

    Text Solution

    |

  5. Let f'(x)=(192x^(3))/(2+sin^(4)pix) for all x epsilonR with f(1/2)=0. ...

    Text Solution

    |

  6. The option(s) with the values of aa n dL that satisfy the following eq...

    Text Solution

    |

  7. Let F:RtoR be a thrice differntiable function. Suppose that F(1)=0,F(3...

    Text Solution

    |

  8. Let F : R to R be a thrice differentiable function . Suppose that F(...

    Text Solution

    |

  9. Let F(x)=intx^[x^2+pi/6](2cos^2t)dt for all x in R and f:[0,1/2] -> [0...

    Text Solution

    |

  10. The total number for distinct x epsilon[0,1] for which int(0)^(x)(t^(2...

    Text Solution

    |

  11. Evaluate: int(-pi//2)^(pi//2)(x^2cosx)/(1+e^x)dx

    Text Solution

    |

  12. Area of the region {(x,y) in R^(2):ygesqrt(|x+3|),5ylex+9le15} is eq...

    Text Solution

    |

  13. Let f:Rto(0,1) be a continuous function. Then, which of the following ...

    Text Solution

    |

  14. Let f: R -> R be a differentiable function such that f(0) = 0,f(pi/2)=...

    Text Solution

    |

  15. If Isum(k=1)^(98)intk^(k+1)(k+1)/(x(x+1))dx ,t h e n: (a) I<(49)/(50...

    Text Solution

    |

  16. If the line x = alpha divides the area of region R = {(x,y) in R^(2) :...

    Text Solution

    |

  17. If g(x)=int(sinx)^("sin"(2x))sin^(-1)(t)dt ,t h e n : (a) g^(prime)(...

    Text Solution

    |

  18. For each positive integer n let y(n)=1/n((n+1)(n+2)…..(n+n)^(1//n))....

    Text Solution

    |

  19. A farmer F(1) has a land in the shape of a triangle with vertices at P...

    Text Solution

    |

  20. The value of the integral int(0)^(1//2)(1+sqrt(3))/(((x+1)^(2)(1-x)^(6...

    Text Solution

    |