If $f(x)=\displaystyle\int_0^{x} t\sin t\,dt$, then $f'(x)$ is

Question

Accepted Answer

B. $x\sin x$

1. By the First Fundamental Theorem, if $f(x)=\int_a^x g(t)\,dt$ then $f'(x)=g(x)$.
2. Here $g(t)=t\sin t$.
3. So $f'(x)=x\sin x$.
4. Options A and D mistakenly differentiate the integrand.
_Source: syllabus Mathematics Ch 7 "Integrals", p.341_

Answer

$\cos x+x\sin x$

Answer

$x\cos x$

Answer

$\sin x+x\cos x$

If $f(x)=\displaystyle\int_0^{x} t\sin t\,dt$, then $f'(x)$ is

Keep practising Straight Lines and Conic Sections