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The value of integral sum (k=1)^(n) int...

The value of integral ` sum _(k=1)^(n) int _(0)^(1) f(k - 1+x) dx ` is

A

` int _(0)^(1) (x) dx`

B

`int _(0)^(2) f(x) dx`

C

` int _(0)^(n) f(x) dx`

D

` n int _(0)^(1) f(x) dx`

Text Solution

Verified by Experts

The correct Answer is:
C
Let `l=int_(0)^(1)f(k-1+x)dx`
`rArr" "l=int_(k-1)^(k)f(t)dt," where "t=k-1+x`
`rArr" "l=int_(k-1)^(k)f(x)dx`
`therefore sum_(k=1)^(n)int_(k-1)^(k)f(x)dx=int_(0)^(1)f(x)dx+int_(1)^(2)f(x)dx+…+int_(n-1)^(n) f(x)dx=int_(0)^(n)f(x)dx`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-PRACTICE EXERCISE (Exercise 2) (MISCELLANEOUS PROBLEMS)
  1. Evaluate the following limit: lim(nto oo)[(n!)/(n^(n))]^(1//n)

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  2. Let a, b and c be non - zero real numbers such that int (0)^(3) (3ax...

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  3. The value of integral sum (k=1)^(n) int (0)^(1) f(k - 1+x) dx is

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  4. Ifint(sinx)^1t^2f(t)dt=1=1-s inx ,w h e r ex in (0,pi/2), then find t...

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  5. The value of int (2)^(4) { |x-2|+|x-3|} dx is

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  6. int (-1)^(2) |x|^(3) dx is equal to

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  7. int (0)^(3) (3x+1)/(x^(2)+9) dx =

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  8. int (0)^(pi//4) ( 4 sin 2 theta d theta )/(sin^(4) theta +cos^(4) thet...

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  9. The value of the integral int (-a)^(a) (xe^(x^(2)))/(1+x^(2)) dx is

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  10. int (-pi//2)^(pi//2) (dx)/(1+cosx) is equal to

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  11. The value of int (0)^(12a) (f(x))/(f(x)+f(12a-x))dx is

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  12. If kint(0)^(1)xf(3x)dx=int(0)^(3)tf(t)dt, then the value of k is

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  13. lim(nto oo)+(1)/(sqrt(n^(2)+n))+(1)/(sqrt(n^(2)+2n))+...(1)/(sqrt(n^(2...

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  14. lim(n->oo) (1^p+2^p+3^p+...........+n^p)/n^(p+1)

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  15. Evaluate: ("lim")(nvecoo)(1/(sqrt(4n^2-1))+1/(sqrt(4n^2-2^2))++1/(sqrt...

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  16. If f(x) = tanx-tan ^(3) x + tan^(5) x - tan ^(7) x + ... infty for o...

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  17. The value of int(0)^((pi)/(8))cos^(3)4 theta d theta is equal to -

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  18. int (0)^(pi//3) (cos x + sin x)/(sqrt(1+sin 2x))dx is equal to

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  19. int (0)^(1) x^(3//2) sqrt(1-x) dx is equal to

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  20. The value of int (1)^(2) (dx)/((x+1) sqrt((x^2)-1)) is

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