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AAKASH SERIES-DEFINITE INTEGRALS-EXERCISE - II
- If [x] represents greatest integer le x then int(1)^(3//2) [2x +1]dx=
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- int(0)^(2) [x^(2)-1]dx=
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- If [x] represents greatest integer le x then int(0)^(sqrt(2))[x^(2)]dx...
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- The value of int(1)^(a)[x] f' (x) dx, a gt 1, where [x] denotes the gr...
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- sum(n=1)^(100) int(n-1)^(n) e^(x-[x])dx=
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- int(0)^(100)sin(x-[x])pidx=
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- int(0)^([x])(2^(x))/(2^[x])dx=
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- int(0)^(3) sqrt((x^(3))/(3-x))dx=
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- int(0)^(a)x^(3)(ax-x^(2))^(3//2)dx=
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- int(0)^(pi//2) x sin^(8) 2x dx=
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- int(0)^(2pi) x sin^(6) x cos^(5) x dx=
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- int(0)^(oo) (x^(3))/((1+x^(2))^(9//2))dx=
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- If I(n) = int(0)^(pi//4) Tan^(n) x dx then I(2)+I(4), I(3)+I(5), I(4)+...
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- If I(n)=int(0)^(pi//4) tan^(n) x dx then {:(" " Lt),(n rarr oo):}n(I(n...
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- I(m, n)= int(0)^(1) x^(m) (ln x)^(n) dx=
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- Lt(xto0)(x^(2))/(int(0)^(x)Tan^(-1)tdt)
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- {:(" " Lt),(x rarr 0):} (int(0)^(x^(2))sec^(2) t dt)/(x sin x) =
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- Let f:RtoR be a differentiable function having f(2)=6,f'(2)=(1)/(48).T...
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- Let P(x) be a function defined on R such that P(x) = P'(1--x), AA x in...
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- If I(1) = int(1)^(2)(dx)/(sqrt(1+x^(2))) and I(2)= int(1)^(2) (dx)/(x)...
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