JEE MAIN Definite Integration Previous Year Questions (PYQs) – Page 17 of 17
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The value of $\displaystyle \int_{-1}^{1}\frac{(1+\sqrt{|x|}-x)e^{x}+(\sqrt{|x|}-x)e^{-x}}{e^{x}+e^{-x}},dx$ is equal to
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Solution
Let f : R $ \to $R be a continuously differentiable function such that f(2) = 6 and f'(2) = ${1 \over {48}}$. If $\int\limits_6^{f\left( x \right)} {4{t^3}} dt$ = (x - 2)g(x), then $\mathop {\lim }\limits_{x \to 2} g\left( x \right)$ is equal to :
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Solution
The value of the integral $\int\limits_{ - 1}^1 {\log \left( {x + \sqrt {{x^2} + 1} } \right)dx} $ is :
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The value of $\int_{e^2}^{e^4} \frac{1}{x}\left(\frac{e^{\left(\left(\log _e x\right)^2+1\right)^{-1}}}{e^{\left(\left(\log _e x\right)^2+1\right)^{-1}}+e^{\left(\left(6-\log _e x\right)^2+1\right)^{-1}}}\right) d x$ is
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Solution
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