If the area bounded by the curve y=f(x),...

If the area bounded by the curve y=f(x), x-axis and the ordinates x=1 and x=b is (b-1) `sin`(3b+4), then find f(x).

f(x)=cos(3x+4)+3(x-1)sin(3x+4)

f(x)=sin(3x+4)+3(x-1)cos(3x+4)

f(x)=sin(3x+4)-3(x-1)cos(3x+4)

None of these

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Verified by Experts

We have
`overset(b)underset(1)(int)"f"(x)dx=(b-1)sin(3b+4)`
differentiate both side w.r.t. b
`"f"(b).1-0=(b-1).3cos(3b+4)+sin(3b+4).1`
`"f"(b)=3(b-1)cos(3b+4)+sin(3b+4)`
`"f"(x)=3(x-1)cos(3x+4)+sin(3x+4)`

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