Let f : [0, 2] → R be a function which is continuous on [0, 2] and is differentiable on…
Mathematics · JEE Advanced · NTA Exams — Limit, Continuity and Differentiability
Let f : [0, 2] → R be a function which is continuous on
[0, 2] and is differentiable on (0, 2) with f (0) = 1 . Let \[F(x)=\int_{0}^{x^{2}} f(\sqrt{t}) d t\] for x ∈ [0, 2]. If F′(x) = f ′(x) for all
x ∈ (0, 2), then F(2) equals
[0, 2] and is differentiable on (0, 2) with f (0) = 1 . Let \[F(x)=\int_{0}^{x^{2}} f(\sqrt{t}) d t\] for x ∈ [0, 2]. If F′(x) = f ′(x) for all
x ∈ (0, 2), then F(2) equals
- e2 – 1
- e4 – 1
- e – 1
- e4
Answer
(B) e 4 – 1
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