Q. $\frac{d}{dx}\int_{f(x)}^{g(x)}{h(t)}\ dt$ is equal to
A) $g^{'}(x)h\left\lbrack g(x) \right\rbrack$
B) $h\left\lbrack g(x) \right\rbrack - h\left\lbrack f(x) \right\rbrack$
C) $g^{'}(x)h\left\lbrack g(x) \right\rbrack - f^{'}(x)h\lbrack f(x)\rbrack$
D) None of the above
Explanation
(c)
$\frac{d}{dx}\int_{f(x)}^{g(x)}h(t)dt = h\left\lbrack g(x) \right\rbrack g^{'}(x) - h\lbrack f(x)f^{'}(x)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.