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For any real number x, let [x] denote th...

For any real number x, let [x] denote the largest less than or equal to x. Let f be a real valued function defined on the interval `[-10, 10]` by `f(x) = {(x-[x]",","if [x] is odd"),(1+[x]-x",","if [x] is even"):}`
Show that `int_(-10)^(10) f(x) cos pi dx = 4`

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AAKASH SERIES-DEFINITE INTEGRALS-Exercise (Level-2)
  1. Show that int(0)^(pi//2) (cos x)/((1+sin x)(2+sin x)) dx = log((4)/(3...

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  2. Show that int(1)^(7thsqrt(2))(1)/(x(2x^(7) + 1))dx=(1)/(7) log((6)/(5)...

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

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  4. Show that int(0)^(1//3)(dx)/((1+x^(2))sqrt(1-x^(2))) = (pi)/(4sqrt(2))

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  5. Show that int(0)^(1)(dx)/((1+x^(2))sqrt(2+x^(2))) = (pi)/(6)

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  6. Show that int(0)^(1//2) (dx)/((1-2x^(2))sqrt(1-x^(2))) = (1)/(2) log(2...

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  7. int(0)^(log5)(e^(x)sqrt(e^(x)-1))/(e^(x)+3)dx=

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  8. Show that int(0)^(pi//2) (cos^(2) theta)/(cos^(2) theta + 4 sin^(2)...

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  9. Show that int(0)^(pi//4) sqrt(tan theta) d theta = (1)/(sqrt(2)) log(s...

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

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  11. Show that int(0)^(pi//2)(sinxcos x)/(1+sin^(4)x)dx = (pi)/(8)

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  12. Prove that int(0)^(pi//2)(cos^(2) x sin x)/(sqrt(1+cos^(2)x))dx = (sqr...

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

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  14. int(0)^(pi//4)[sqrt(tan x) + sqrt(cot x)] = dx

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

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  16. Find the value of Lim(x rarr 0) (1)/(x^(3)) int(0)^(x) (t(ln (1+t)))/...

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  17. Find the value of int(0)^(1)(x^(4)(1-x)^(4))/(1+x^(2))dx

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

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

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

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