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Let f(x)={:{(1-|x|","|x|le 1),(0","" ...

Let `f(x)={:{(1-|x|","|x|le 1),(0","" "|x|gt1):}` and, g(x)=f(x-1)+f(x+1) for all `x in R`. Then, the value of `int_(-3)^(3) g(x)dx`, is

A

2

B

3

C

4

D

5

Text Solution

Verified by Experts

The correct Answer is:
A
The graph of f(x) and g(x) are shown in Fig. 14 and 15 respectively.

Clearly,
`overset(3)underset(-3)int g(x)dx=overset(-2)underset(-3)int 0 dx+overset(0)underset(-2)int f(x)dx+overset(2)underset(0)intf(x)dx+overset(3)underset(2)int 0 dx`
`rArr overset(3)underset(-3)intg(x) dx=2overset(2)underset(0)int f(x) dx=2((1)/(2)xx2xx1)=2`
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OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Section I - Solved Mcqs
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  13. The value int^(2)(-2) {p" In"((1+x)/(1-x))+q" In "((1-x)/(1+x))-2+r}...

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  14. 7(int0^1(x^4(1-x)^4dx)/(1+x^2)+pi) is equal to

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  15. The value of lim(x to 0)(1)/(x^(3))(t " In"(1+t))/(t^(4)+4)dt is

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  18. For any real number x, let [x] denote the largest integer less than or...

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  19. Let of a real-valued function defined on the interval(0,oo) by f(x)=In...

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