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If for every integer n, int(n)^(n+1) f(x...

If for every integer n, `int_(n)^(n+1) f(x)dx=n^(2)`, then the value of
`int_(-2)^(4) f(x)dx`, is

A

16

B

14

C

19

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
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OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Exercise
  1. If F(x)=(1)/(x^(2))int(4)^(x) [4t^(2)-2F'(t)]dt then F'(4) equals

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  2. If f(x) is an odd function defined on [-T//2,T//2] and has period T, t...

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  3. If for every integer n, int(n)^(n+1) f(x)dx=n^(2), then the value of ...

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  4. int(-pi+4)^(pi//4) (tan^(2)x)/(1+a^(x))dx is equal to

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  5. The value of int(0)^(pi//2) cosec(x-pi//3)cosec(x-pi//6)dx is

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  6. The value of int(-1)^(1) x|x|dx, is

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  7. int0^3 |x^(3)+x^(2)+3x|dx is equal to

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  8. The value of the integral int(0)^(3) (dx)/(sqrt(x+1)+sqrt(5x+1)) is

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  9. int(1)^(-1) (x^(3)+|x|+1)/(x^(2)+2|x|+1)dxis equal to

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  10. int(-pi/2)^(pi//2) log(e ){((ax^(2)+bx+c)/(ax^(2)-bx+c))(a+b)|sinx|}dx...

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  11. For any natural number n, the value of the integral int(0)^(sqrt(n))...

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  12. For any n in R^(+), the value of the integral int(0)^(n[x]) (x-[x])d...

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  13. If phi'(x)=(log(e )|sin x|)/(x),x ne pi,n in Z and int(1)^(3) (3log(...

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  14. The equation int(-pi//4)^(pi//4) {a|sin x|+(b sin x)/(1+cos x)+c}dx=...

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  15. Let f(x) be a continuous function such that f(a-x)+f(x)=0 for all x i...

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  16. The value of int(alpha)^(beta) x|x|dx, where a lt 0 lt beta, is

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  17. int(-pi//2)^(pi//2) (|x|)/(8 cos^(2)2x+1)dxhas the value

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  18. If [.] denotes the greatest integer function and f(x)={:{(3[x]-(5|x|...

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  19. Find the value of int(-1)^1[x^2+{x}]dx ,w h e r e[dot]a n d{dot} denot...

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  20. The value of int(-1)^(1)sin^(-1)[x^(2)+(1)/(2)]dx+int(-1)^(1) cos^(-...

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