Basic Maths Grand Test- Q5

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 If \ \ \ f(a+b-x) = f(x) , then \int_{a}^{b} {xf(x)} dx \ \ \ equals

A. \frac{a+b}{2} \int_{a}^{b} {f(b-x)} dx

B. \frac{a+b}{2} \int_{a}^{b} {f(b+x)} dx

C. \frac{b-a}{2} \int_{a}^{b} {f(x)} dx

D. \frac{a+b}{2} \int_{a}^{b} {f(x)} dx

asked Nov 17, 2019 in Basic Maths by gbmentor (90,880 points) 1 flag
edited Jun 11 by deepak-gatebook

3 Answers

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ANS should be C.

Correct formula is Option C not D.


answered Nov 20, 2019 by bhargavakapilpro20 (14,660 points)
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Let\ P=\int_{a}^{b}x*f(x)dx

Let's\ use\ the\ corollary \int_{a}^{b}g(x)dx=\int_{a}^{b}g(a+b-x)dx


P=(a+b)\int_{a}^{b}f(a+b-x)dx - \int_{a}^{b}x*f(a+b-x)dx

Also\ it\ is\ given\ that\ f(a+b-x)=f(x)

P=(a+b)\int_{a}^{b}f(x)dx - \int_{a}^{b}x*f(x)dx

P=(a+b)\int_{a}^{b}f(x)dx - P



Option D is correct

answered Nov 20, 2019 by (2,920 points)
edited Nov 21, 2019 by
0 votes

Formula told by Sir in the video of Gatebook- 

Note- See formula no. (4) in image.]

Video no-  Calculs- part 8

Correct ans C.

answered Nov 20, 2019 by bhargavakapilpro20 (14,660 points)
No bro. It is not correct.
That is the SS from Gatebook Basic Maths video only.

@getgatebook @kiran