Failed to connect to MySQL: Access denied for user 'examnext_online'@'localhost' (using password: YES) 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(sqrtt)dt`for x `in` [0,2]. If F'(x)=f'(x) for all x `in` (0,2), then F(2) equals - Sarthaks eConnect
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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(sqrtt)dt`

for x `in` [0,2]. If F'(x)=f'(x) for all x `in` (0,2), then F(2) equals 

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(sqrtt)dt`

for x `in` [0,2]. If F'(x)=f'(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`

Solution

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Best answer

`=> f(x)=e^4 and F'(x)=f'(x)=>F(X)=f(x)+c=>F(x)=f(x)-1(text(since)    F(0)=0)`

so, `F(2)=f(2)-1=e^4-1`

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