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+1 vote
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in Definite Integrals by (30.0k points)
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\(\int\limits_{0}^{2a} \)f(x) dx equal to 

A. 2\(\int\limits_{0}^{a} \)f(x)dx

B 0

C. \(\int\limits_{0}^{a} \)f(x)dx + \(\int\limits_{0}^{a} \)f(2a - x)dx

D.  \(\int\limits_{0}^{a} \)f(x)dx + \(\int\limits_{0}^{2a} \)f(2a - x)dx

1 Answer

+2 votes
by (28.8k points)
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Best answer

Correct option is C. \(\int\limits_{0}^{a} \)f(x)dx + \(\int\limits_{0}^{a} \)f(2a - x)dx

We know that

Let, t = 2a – x ⇒ x = 2a - t

Differentiating both side with respect to x

\(\cfrac{dt}{dx}=-1\)

⇒dx = -dt

At x = a, t =a

At x = 2a, t = 0

The final is y = A + B

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