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The value of int(-2)^(2) |[x]| dx is equ...

The value of `int_(-2)^(2) |[x]| dx` is equal to

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
D
We have,
`I=overset(2)underset(-2)int |[x]|dx`
`rArr I=overset(-1)underset(-2)int |-2|dx+overset(0)underset(-1)int |-1|dx+overset(1)underset(0)int |0|dx+overset(2)underset(1)int |1|dx`
`rArr I=2overset(-1)underset(-2)int dx+overset(0)underset(-1)int dx+overset(1)underset(0)int 0dx+overset(2)underset(1)int 1 dx`
`rArr I=2(-1+2)+(0+1)+0+(2-1)=2+1+=4`
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OBJECTIVE RD SHARMA ENGLISH-DEFINITE INTEGRALS-Section I - Solved Mcqs
  1. The integral underset(0)overset(pi)int x f(sinx )dx is equal to

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  2. If f(x) =(e^x)/(1+e^x), I1=int(f(-a))^(f(a)) xg(x(1-x))dx, and I2=int(...

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  3. The value of int(-2)^(2) |[x]| dx is equal to

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  4. The value int^(2)(-2) {p" In"((1+x)/(1-x))+q" In "((1-x)/(1+x))-2+r}...

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  5. 7(int0^1(x^4(1-x)^4dx)/(1+x^2)+pi) is equal to

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  6. The value of underset(xrarr0)(lim)(1)/(x^(3)) int(0)^(x)(tln(1+t))/(t^...

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  7. Let f be the function defined on [-pi,pi] given by f(0)=9 and f(x)=sin...

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  8. Let f be a real valued functional defined on the interval (-1,1) such ...

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

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  10. about to only mathematics

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  11. Let p(x) be a function defined on R such that p'(x)=p'(1-x) for all x ...

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  12. If inta^b(f(x)-3x)dx=a^2-b^2 then the value of f(pi/6) is

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  13. The value of (pi^2)/(1n3)int(7/6)^(5/6)sec(pix)dxi s

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  14. The value of the integral int(-pi//2)^(pi//2) (x^(2) + log" (pi-x)/(pi...

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  15. Let f :(0,1) to (0,1) be a differentiable functino such that f '(x) ne...

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  16. The value of the integral int(0)^(2) (log(x^(2)+2))/((x+2)^(2)), dx is

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  17. The following integral int(pi/4)^(pi/2)(2cos e cx)^(17)dx is equal to ...

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  18. Let f:[0,2]vecR be a function which is continuous on [0,2] and is diff...

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  19. Given that for each a epsilon(0,1),lim(hto 0^(+)) int(h)^(1-h)t^(-a)(1...

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  20. Given that for each a epsilon(0,1),lim(hto 0^(+)) int(h)^(1-h)t^(-a)(1...

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