Class 12

30.Definite Integral question bank (Maths)

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Q1.

If \(f(x)\) be a periodic function with period \(T\) so that \(f(x+13)+f(x+630)=0\) and\(\sum_{p=1}^{777}\int_{p}^{p+T}f(x)dx = \lambda \int_{0}^{T}f(x)dx,\)then

(A)
\(T=1234\)
(B)
\(\lambda + T = 2011\)
(C)
\(\lambda\ \&\ T\) both are prime
(D)
only \(\lambda\) is prime
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Q2.

Which of the following have same value?

(A)
\(\displaystyle \int_{2}^{e} \frac{1-\log x}{(\log x)^2}\,dx\)
(B)
\(\displaystyle \int_{0}^{\pi/4} x\sec^2 x\,dx\)
(C)
\(\displaystyle \int_{0}^{1/\sqrt{2}} \frac{\sin^{-1}x\,dx}{(1-x^2)^{3/2}}\)
(D)
\(\displaystyle \lim_{n\to\infty}\sum_{r=1}^{n}\frac{n-r}{n^2+r^2}\)
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