Home
Class 12
MATHS
If f(x)=Asin((pix)/2)+b ,f^(prime)(1/2)=...

`If f(x)=Asin((pix)/2)+b ,f^(prime)(1/2)=sqrt(2)a n d` `int_0^1f(x)dx=(2A)/pi` the constants A and B are (a) `pi/2a n dpi/2` (b) `2/pia n d3/pi` (c) `0a n d-4/pi` (d) `4/pia n d0`

A

`(pi)/(2) and (pi)/(2)`

B

`(2)/(pi) and (3)/(pi)`

C

`0 and -(4)/(pi)`

D

`(4)/(pi) and 0`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test 1|57 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|87 Videos

  • DERIVATIVE AS A RATE MEASURER

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|26 Videos

Similar Questions

Explore conceptually related problems

If f^(prime)(1)=-2sqrt(2)a n dg^(prime)(sqrt(2))=4 , then the derivative of f(tanx) with respect to g(secx) at x=pi/4, is 1 (b) -1 (c) 2 (d) 4

If int_0^pi x f(sinx) dx=A int_0^(pi/2) f(sinx)dx , then A is (A) pi/2 (B) pi (C) 0 (D) 2pi

int_0^(pi//2)1/(1+cot^3x)dx is equal to a 0 b. 1 c. pi//2 d. pi//4

int_0^oo(x dx)/((1+x)(1+x^2)) is equal to (A) pi/4 (B) pi/2 (C) pi (D) none of these"

If f(x) = xsinx , then f'(pi/2) is a. 1/2 b. 1 c. 0 d. -1

If f^(prime)(1)=-2sqrt(2) and g^(prime)(sqrt(2))=4 , then the derivative of f(tanx) with respect to g(secx) at x=pi/4, is: (a)1 (b) -1 (c) 2 (d) 4

If A-B=pi//4 , then (1+t a n A)(1-t a n B) is equal to 2 b. 1 c. 0 d. 3

If x in[(4n+1)(pi)/(2),(4n+3)(pi)/(2)] and n in N , then the value of int_(0)^(x) [cos t] dt , is

The value of int_0^pi (sin(n+1/2)x)/(sin (x/2)) dx is, (a) n in I, n >= 0 pi/2 (b) 0 (c) pi (d) 2pi

int_0^1d/(dx){sin^(-1)((2x)/(1+x^2))}dx is equal to 0 (b) pi (c) pi//2 (d) pi//4

OBJECTIVE RD SHARMA ENGLISH-DEFINITE INTEGRALS-Chapter Test 2
  1. If int(0)^(x^(2)) sqrt(1+t^(2)) dt, then f'(x)n equals

    Text Solution

    |

  2. The value of integral int(1)^(e) (log x)^(3)dx , is

    Text Solution

    |

  3. If int(x^(2))^(x^(4)) sin sqrt(t) dt, f'(x) equals

    Text Solution

    |

  4. lim(n-gtoo)[(1+1/n)(1+2/n)(1+n/n)]^(1/n)

    Text Solution

    |

  5. underset(nrarroo)("lim")[(1+(1)/(n^(2)))(1+(2^(2))/(n^(2)))"....."(1+(...

    Text Solution

    |

  6. If int0^1 e^(x^2)(x-alpha)dx=0, then (a)alphalt2 (b)alphalt0 (c)"" 0l...

    Text Solution

    |

  7. If f(x) satisfies the requirements of Rolle's Theorem in [1,2] and f(x...

    Text Solution

    |

  8. The value of the integral int(0)^(1) cot^(-1) (1-x+x^(2))dx, is

    Text Solution

    |

  9. The integral int(-1)^(1) (|x+2|)/(x+2)dx is equal to

    Text Solution

    |

  10. Let I= int(0)^(1) (e^(x))/( x+1) dx, then the vlaue of the intergral ...

    Text Solution

    |

  11. Evaluate int(0)^(pi)(x dx)/(1+cos alpha sin x),where 0lt alpha lt pi.

    Text Solution

    |

  12. int(pi)^(10n) |sin x|dx is equla to

    Text Solution

    |

  13. about to only mathematics

    Text Solution

    |

  14. If int(0)^(oo)e^(-ax)dx=(1)/(a)," then "int(0)^(oo)x^(n)e^(-ax)dx is

    Text Solution

    |

  15. The value of int(0)^(2pi)[2 sin x]dx, where [.] represent the greatest...

    Text Solution

    |

  16. If f(x)=Asin((pix)/2)+b ,f^(prime)(1/2)=sqrt(2)a n d int0^1f(x)dx=(2A...

    Text Solution

    |

  17. If I(m,n)= int(0)^(1) x^(m) (ln x)^(n)dx then I(m,n) is also equal to

    Text Solution

    |

  18. lim(n->oo)(1^(99)+2^(99)+3^(99)+.......n^(99))/(n^(100))=

    Text Solution

    |

  19. I(n)=int(0)^(pi//4)tan^(n)xdx, then lim(n to oo)n[I(n)+I(n+2)] equals ...

    Text Solution

    |

  20. Let int(0)^(a)f(x)dx = lambda and int(0)^(a)f(2a-x)dx=mu. Then int(0)^...

    Text Solution

    |