Question

The area bounded by the curves `y=f(x),` the x-axis, and the ordinates `x=1a n dx=b` is `(b-1)sin(3b+4)dot` Then `f(x)` is. `(x-1)cos(3x+4)` `sin(3x+4)` `sin(3x+4)+3(x-1)cos(3x+4)` None of these
A. `(x-1)cos(3x+4)`
B. `8sin(3x+4)`
C. `sin(3x+4)+3(x-1)cos(3x+4)`
D. None of the above

Answer 1

Correct Answer - C
Since, `int_(1)^(b)f(x)dx=(b-1)sin(3b+4)`
On differentiating both sides w.r.t. b, we get
`f(b)=3(b-1)*cos(3b+4)+sin(3b+4) `
` therefore f(x)=sin(3x+4)+3(x-1)cos(3x+4)`