Let f(x) be a continuous function and I ...

Let `f(x)` be a continuous function and `I = int_(1)^(9) sqrt(x)f(x) dx`, then

There exists some `c in (1,9 )` such that `I = 8sqrt(c) f(c)`

There exists some `p,q in (1,3)` such that `I = 2[p^(2)f(p^(2))+q^(2)f(q^(2))]`

There exists some `alpha in (1,9)` such that `I = 9sqrt(x)f(alpha)`

If `f(x) ge 0 AA x in [1,9] rArr I gt 0`

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RESONANCE ENGLISH-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 2 Part - III

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Let I(n) = int(0)^(pi)(sin^(2)(nx))/(sin^(2)x)dx, n in N then
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Let f(x) be a continuous function and I = int(1)^(9) sqrt(x)f(x) dx, t...
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Let A = int(1)^(e^(2))(lnx)/(sqrt(x))dx, then
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Let L(1) = lim(xrarr0^(+)) (int(0)^(x^(2)) sinsqrt(t)dt)/(x-sinx), the...
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lim(nrarroo) ((1^(k)+2^(k)+3^(k)+"......"n^(k)))/((1^(2)+2^(2)+"....."...
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Let T(n) = sum(r=1)^(n) (n)/(r^(2)-2r.n+2n^(2)), S(n) = sum(r=0)^(n)(n...
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A function f(x) satisfying int(0)^(1) f(tx)dt=n f(x), where xgt0, is
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Find the area bounded by y=sin^(-1)x ,y=cos^(-1)x ,and the X-axis.
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