Question

\[If~\int\limits f(x)~sinx~dx~=~-f(x)cosx+\int\limits 3x^2cosx~dx\]then f(x) could be
a) 3x^2
b) x^3
c) -x^3
d) sinx
e) cosx

Answer 1

Could someone check my work? o-o

uv - ∫v du

if dv = sinx dx then v = -cosx
and then if du = 3x^2 dx
then u = 3(1/3)x^3 = x^3

so... B ?

Answer 2

your question is
\[f(x)=\int\limits 3 x^2~dx=\frac{ 3 x^3 }{ 3 }=x^3\]
again you are correct.

Answer 3

yw