Question

The anti – derivative of the function (3x + 4) |sin x|, when $0<x<\pi$, is given by

• A. $3sinx-(3x+4)cosx+c$
• B. $3sinx+(3x+4)cosx+c$
• C. $-3sinx-(3x+4)cosx+c$
• D. None of these

Answer 1

The correct option is A $3sinx-(3x+4)cosx+c$

In the interval $(0,\pi )$, sin x is positive, therefore, $(3x+4)|sinx|=(3x+4)sinx$.
$\therefore$ The antiderivative of $(3x+4)|sinx|$ is
$=\int (3x+4)sinxdx=-(3x+4)cosx+\int 3cosxdx=-(3x+4)cosx+3sinx+c$