AP EAMCET · Maths · Definite Integration
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 \(F(h(t)) h^{\prime}(t)-F(g(t)) g^{\prime}(t)\)
- D \(f(h(t)) h^{\prime}(t)-f(g(t)) g^{\prime}(t)\)
Answer & Solution
Correct Answer
(D) \(f(h(t)) h^{\prime}(t)-f(g(t)) g^{\prime}(t)\)
Step-by-step Solution
Detailed explanation
\(\frac{d}{d t} \int_{g(t)}^{h(t)} f(x) d x=f(h(t)) \cdot h^{\prime}(t)-f\left(g(t) \cdot g^{\prime}(t)\right.\) (by Newton - Leibnitz theorem)
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