JEE MAIN Indefinite Integration Previous Year Questions (PYQs) – Page 5 of 5
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If $\displaystyle \int x^{5}e^{-x^{2}},dx=g(x)e^{-x^{2}}+c$, where $c$ is a constant of integration, then $g(-1)$ is equal to:
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Solution
The integral $\displaystyle \int \frac{dx}{(1+\sqrt{x})\sqrt{x - x^{2}}}$ is equal to :
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Solution
If $\displaystyle \int e^{x}\!\left(\frac{x\sin^{-1}x}{\sqrt{1-x^{2}}}+\frac{\sin^{-1}x}{(1-x^{2})^{3/2}}+\frac{x}{1-x^{2}}\right)\!dx=g(x)+C$, where $C$ is the constant of integration, then $g\!\left(\dfrac{1}{2}\right)$ equals:
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Solution
Let $n\ge 2$ be a natural number and $0<\theta<\dfrac{\pi}{2}$. Then
\[
\int \frac{\big(\sin^{n}\theta-\sin\theta\big)^{1/n}\,\cos\theta}{\sin^{\,n+1}\theta}\,d\theta
\]
is equal to (where $C$ is a constant of integration):
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Solution
The integral $\displaystyle \int \dfrac{2x^3 - 1}{x^4 + x} , dx$ is equal to :
(Here $C$ is a constant of integration)
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Solution
The integral $\displaystyle \int \frac{dx}{x^{2}(x^{4}+1)^{3/4}}$ equals :
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Solution
If $\int {{{\cos \theta } \over {5 + 7\sin \theta - 2{{\cos }^2}\theta }}} d\theta $ = A${\log _e}\left| {B\left( \theta \right)} \right| + C$,where C is a constant of integration, then ${{{B\left( \theta \right)} \over A}}$can be :
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Solution
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