Question

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

• A. $3\sin x-(3x+4)\cos x+c$
• B. $3\sin x+(3x+4)\cos x+c$
• C. $-3\sin x+(3x+4)\cos x+c$
• D. $3\cos x+(3x+4)\sin x+c$

Answer 1

Answer: (A)

$3\sin x-(3x+4)\cos x+c$

$(3x+4)\left|sinx\right|0<x<\pi$
$\pi >x>0sinx>0$
$\left|sinx\right|=sinx.$
$\int (3x+4)sinx.dx.$
$=(3x+4)\int sinxdx$
$-\int 3(\int sinxdx)dx$
$=-(3x+4)cosx-3\int (-cosx)dx$
$=-(3x+4)cosx+3sinx+c$
$\int (3x+4)\left|sinx\right|dx=3sinx-(3x+4)cosx+c$