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Question

Find the value of 02f'(x2)2xdx


A

f(4)f(0)

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B

f(4)+f(0)

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C

f(0)f(4)

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D

None of these

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Solution

The correct option is A

f(4)f(0)


An explanation for the correct option:

Step 1: Convert the integrand to f(m)dm using substitution

We need to find the value of 02f'(x2)2xdx

Let, x2=m

Differentiation w.r.to x.

2xdx=dm

Step 2: Convert the limits of integration to the corresponding values of m.

Also, for x=0,

m=02m=0

and for x=2,

m=22m=4

Step 3: Evaluate the integral in terms of m.

So given integration would be,

=04f'(m)dm=[f(m)]04=f(4)-f(0)

Therefore, option (A) is the correct answer.


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