Q115 / 160 · AP EAMCET 2022 (07 Jul Shift 1) · Mathematics
If $\int f(x) d x=F(x)+C$, then $\frac{d}{d t} \int_{g(t)}^{h(t)} f(x) d x=$
- A$f(h(t))-f((t))$
- B$F(h(t))-F(g(t))$
- C$F(h(t)) h^{\prime}(t)-F(g(t)) g^{\prime}(t)$
- Correct answerD$f(h(t)) h^{\prime}(t)-f(g(t)) g^{\prime}(t)$
Solution
$\frac{d}{d t} \int_{g(t)}^{h(t)} f(x) d x=f(h(t)) \cdot h^{\prime}(t)-f\left(g(t) \cdot g^{\prime}(t)\right.$
(by Newton - Leibnitz theorem)
Hence, the correct answer is option: 'D'.