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Question 340010
JEE Mathematics · Hard

Definite Integration and Area: Leibniz rule MCQ

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Leibniz ruleHardQuestion 340010

Question

d/dx ∫ₐ^(g(x)) f(t) dt equals:
  1. A
    f(g(x)) × g'(x)
    Correct
  2. B
    f(g(x))
  3. C
    g'(x)
  4. D
    ∫ₐ^(g(x)) f'(t) dt

Correct answer

f(g(x)) × g'(x)

Explanation

Leibniz differentiation under the integral sign: d/dx ∫ₐ^(g(x)) f(t) dt = f(g(x)) × g'(x) (by the chain rule applied to the Fundamental Theorem of Calculus).

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