JEE MAIN Definite Integration Previous Year Questions (PYQs) – Page 16 of 17
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$ \text{The value of } \displaystyle \int_{\pi/3}^{\pi/2} \frac{2+3\sin x}{\sin x\,(1+\cos x)}\,dx \text{ is equal to:} $
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Solution
The value of the definite integral $\int\limits_{\pi /24}^{5\pi /24} {{{dx} \over {1 + \root 3 \of {\tan 2x} }}} $ is :
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Solution
The value of $\int_{0}^{1} (2x^{3} - 3x^{2} - x + 1)^{\frac{1}{3}} \, dx$ is equal to:
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Solution
The area (in sq. units) of the region, given by the set $\{ (x,y) \in R \times R|x \ge 0,2{x^2} \le y \le 4 - 2x\} $ is :
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Solution
Let $[t]$ denote the greatest integer less than or equal to $t$.
Then the value of the integral
$\int_{-3}^{101} \left( [\sin(\pi x)] + e^{[\cos(2\pi x)]} \right) dx$ is equal to
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Solution
Let $\alpha>0$. If $\displaystyle \int_{0}^{\alpha}\frac{x}{\sqrt{x+\alpha}-\sqrt{x}}\,dx=\dfrac{16+20\sqrt{2}}{15}$, then $\alpha$ is equal to:
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Solution
If $\displaystyle \int_{0}^{\pi/2} \dfrac{\cot x}{\cot x + \cos \csc x} , dx = m(\pi + n)$, then $m \cdot n$ is equal to
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Solution
Let
$f(x)=
\begin{cases}
-2, & -2 \le x \le 0,\\[4pt]
x-2, & 0 < x \le 2,
\end{cases}$
and $h(x)=f(|x|)+|f(x)|.$
Then $\displaystyle \int_{-2}^{2} h(x)\,dx$ is equal to:
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Solution
The integral $\displaystyle \int_{2}^{4}\dfrac{\log x^{2}}{\log x^{2}+\log(36-12x+x^{2})}\,dx$ is equal to :
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Solution
If $f(x) =
\begin{cases}
\int_{0}^{x} \left( 5 + |1 - t| \right) dt, & x > 2 \\
5x + 1, & x \leq 2
\end{cases}$, then
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Solution
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