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Let f: R rarr R be defined by f(x)=|x-2n...

Let `f: R rarr R` be defined by `f(x)=|x-2n|` if `x in [2 n -1, 2n+1], (n in Z)`. Then show that for any positive integer `n, int_(0)^(2n) f(x)dx=n`.
Hint : f in continuous and periodic with period 2.

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AAKASH SERIES-DEFINITE INTEGRALS-ADDITIONAL EXERCISE
  1. Show that int(0)^(pi//2) (dx)/(3+4 six) = (1)/(sqrt(7)) log((4+sqrt(7)...

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  2. Show that int(e)^(e^(2))(1)/(log x) dx = int(1)^(2)(e^(x))/(x) dx

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  3. Show that int(0)^(pi//4) x cos x cos 3 x dx = (pi-3)/(16)

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  4. Show that int(0)^(pi//2)(cos x)/((1+sin x )(2 + sin x))dx = log (4/3)

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  5. Show that int(0)^(pi//2)(sin x cos x)/(cos^(2) x + 3 cos x + 2) dx = l...

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  6. Show that int(0)^(log 5) (sqrt(e^(x)-1))/(e^(x)+3)e^(x)dx = 4 - pi

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  7. Show that int(0)^(pi/4)(dx)/(cos^(4)x - cos^(2)x sin^(2) x + sin^(4) ...

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  8. Show that int(0)^(oo) (dx)/((x+sqrt(1+x^(2)))^(n))=(n)/(n^(2)-1), (n i...

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  9. Show that int(0)^(pi//4) (sqrt(tan x )+sqrt(cot x))dx= pi/sqrt(2)

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  10. int(0)^(50)e^({x})dx where {x} denotes the fractional part of x

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  11. Evaluate int(0)^(100pi) sqrt((1-cos 2 x)/(2))dx

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  12. Let f(x) be a periodic function with period 1 and integrable over any ...

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  13. Evaluate the following (i) int(0)^(30)[x]dx

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  14. Evaluate the following (ii) int(-2)^(2)[x]dx

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  15. Evaluate the following (iii) int(0)^(5)x[x]dx

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  16. Evaluate the following (iv) int(0)^(1.5)[x^(2)]dx

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  17. Evaluate the following (v) int(0)^(5)[sqrt(x)]dx

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  18. Evaluate the following (vi) int(0)^(25) [sqrt(x)]dx

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  19. int(0)^(50)(x-[x])dx=

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  20. Let f: R rarr R be defined by f(x)=|x-2n| if x in [2 n -1, 2n+1], (n i...

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