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`

Verified by Experts

The correct Answer is:

D

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