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AP EAMCET20227 Jul 2022Morning ShiftMathematicsDefinite IntegrationActual

If f(x) d x=F(x)+C , then d d t _ g(t) ^ h(t) f(x) d x=

Options

  1. Af(h(t))-f((t))
  2. BF(h(t))-F(g(t))
  3. CF(h(t)) h^ (t)-F(g(t)) g^ (t)
  4. Df(h(t)) h^ (t)-f(g(t)) g^ (t)

Correct answer

D. f(h(t)) h^ (t)-f(g(t)) g^ (t)

Step-by-step solution

d d t _ g(t) ^ h(t) f(x) d x=f(h(t)) h^ (t)-f (g(t) g^ (t) . (by Newton - Leibnitz theorem)

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