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 in Basic Maths by gbmentor (85,520 points)
reshown Nov 20 by getgatebook

3 Answers

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ANS should be C.

Correct formula is Option C not D.

 

answered Nov 20 by bhargavakapilpro20 (13,760 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=\int_{a}^{b}(a+b-x)*f(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

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

P=\frac{(a+b)}{2}\int_{a}^{b}f(x)dx

Option D is correct

answered Nov 20 by tspranaykumar562 (2,720 points)
edited Nov 21 by tspranaykumar562
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 by bhargavakapilpro20 (13,760 points)
No bro. It is not correct.
That is the SS from Gatebook Basic Maths video only.

@getgatebook @kiran
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