JEE MAIN Definite Integration Previous Year Questions (PYQs) – Page 5 of 17
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The value of the integral $\displaystyle\int_{\pi/4}^{3\pi/4}\frac{x}{1+\sin x},dx$ is :
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Solution
The value of $\int\limits_0^\pi {{{{e^{\cos x}}\sin x} \over {(1 + {{\cos }^2}x)({e^{\cos x}} + {e^{ - \cos x}})}}dx} $ is equal to:
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If ${I_n} = \int\limits_{{\pi \over 4}}^{{\pi \over 2}} {{{\cot }^n}x\,dx} $, then :
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Let $I_n(x) = \int_0^x \dfrac{1}{(t^2+5)^n} \, dt, \; n = 1, 2, 3, \dots$
Then :
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Let $f$ and $g$ be continuous functions on $[0,a]$ such that $f(x)=f(a-x)$ and $g(x)+g(a-x)=4$. Then $\displaystyle \int_{0}^{a} f(x)\,g(x)\,dx$ is equal to :
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$\int\limits_6^{16} {{{{{\log }_e}{x^2}} \over {{{\log }_e}{x^2} + {{\log }_e}({x^2} - 44x + 484)}}dx} $$ is equal to :
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For $0 < \mathrm{a} < 1$, the value of the integral $\int_\limits0^\pi \frac{\mathrm{d} x}{1-2 \mathrm{a} \cos x+\mathrm{a}^2}$ is :
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The value of $\int\limits_{ - \pi /2}^{\pi /2} {{{{{\cos }^2}x} \over {1 + {3^x}}}} dx$ is :
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The value of $\sum\limits_{n = 1}^{100} {\int\limits_{n - 1}^n {{e^{x - [x]}}dx} } $, where [ x ] is the greatest integer $ \le $ x, is :
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If $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{96 x^2 \cos ^2 x}{\left(1+e^x\right)} \mathrm{d} x=\pi\left(\alpha \pi^2+\beta\right), \alpha, \beta \in \mathbb{Z}$, then $(\alpha+\beta)^2$ equals
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Solution
JEE MAIN
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