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For any real number x ,l e t[x] denote t...

For any real number `x ,l e t[x]` denote the largest integer less than or equal to `x ,L e tf` be a real-valued function defined on the interval `[-10 , 10]` be `f(x)={x-[x],if[x]i sod d1+[x]-x ,if[x]i se v e n` Then the value of `(pi^2)/(10)int_(-10)^(10)f(x)cospixdxi s____`

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VMC MODULES ENGLISH-INTEGRAL CALCULUS - 2 -JEE Advanced (Archive)
  1. Show that int0^(npi+v)|sinx|dx=2n+1-cosv , where n is a positive integ...

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  2. Given a function f(x) such that It is integrable over every interval o...

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  3. For any real number x ,l e t[x] denote the largest integer less than o...

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

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  5. Let f be a non-negative function defined on the interval [0,1]. If int...

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  6. f(x)=int0^x f(t) dt=x+intx^1 tf(t)dt, then the value of f(1) is

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  7. Let f : R to R be a differentiable function and f(1) = 4. Then, the va...

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  8. Consider the statements : P : There exists some x IR such that f(x)...

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  9. Let f (x)= int (x^(2))^(x ^(3))(dt)/(ln t) for x gt 1 and g (x) = in...

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  10. Let f(x)=|secxcosx s e c^2x+cotx cos e c\ x cos^2x cos^2x cos e c^2x1c...

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  11. For x >0,l e tf(x)=int1^x((log)e t)/(1+t)dtdot Find the function...

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  12. Let a+b=4,w h e r ea<2,a n dl e tg(x) be a differentiable function. If...

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  13. Determine a positive integer nlt=5 such that int0^1e^x(x-1)^n=16-6e

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  16. For a epsilonR (the set of all real numbers) a!=-1, lim(n to oo) ((1^(...

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  17. Let S(n)=underset(k=1)overset(n)sum (n)/(n^(2)+nk+k^(2)) and T(n)=unde...

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  18. Show that ("lim")(n vec oo)(1/(n+1)+1/(n+2)++1/(6n))=log6

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