Let f:[0,2]→R be a function which is continuous on [0,2] and is differentiable on (0,2) with f(0)=1Let:F(x)=∫0x2f(t)dtforx∈[0,2]I˙fFprime(x)=fprime(x) . for all x∈(0,2), then F(2) equals (a)e2−1 (b) e4−1(c)e−1 (d) e4

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Let {f}:{[{0},{2}]}{R} be a function which is continuous on [0

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Let $f : [0, 2] \to R$ be a function which is continuous on [0,2] and is differentiable on (0,2) with $f (0) = 1$ $L e t : F (x) = \int_{0}^{x^{2}} f (t) d t f or x \in [0, 2] \dot{I} f F^{p r i m e} (x) = f^{p r i m e} (x)$ . for all $x \in (0, 2),$ then $F (2)$ equals (a) $e^{2} - 1$ (b) $e^{4} - 1$ (c) $e - 1$ (d) $e^{4}$

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Oliver Discussed

Let

f : [0, 2] \to R

be a function which is continuous on [0,2] and is differentiable on (0,2) with

f (0) = 1

L e t : F (x) = \int_{0}^{x^{2}} f (t) d t f or x \in [0, 2] \dot{I} f F^{p r i m e} (x) = f^{p r i m e} (x)

. for all

x \in (0, 2),

then

F (2)

equals (a)

e^{2} - 1

(b)

e^{4} - 1

(c)

e - 1

(d)

e^{4}

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Question Text	Let $f : [0, 2] \to R$ be a function which is continuous on [0,2] and is differentiable on (0,2) with $f (0) = 1$ $L e t : F (x) = \int_{0}^{x^{2}} f (t) d t f or x \in [0, 2] \dot{I} f F^{p r i m e} (x) = f^{p r i m e} (x)$ . for all $x \in (0, 2),$ then $F (2)$ equals (a) $e^{2} - 1$ (b) $e^{4} - 1$ (c) $e - 1$ (d) $e^{4}$
Answer Type	Video solution: 1
Upvotes	150