# Definite Integration · Mathematics · MHT CET

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MHT CET 2023 14th May Evening Shift
If $$I_n=\int_\limits0^{\frac{\pi}{4}} \tan ^n \theta d \theta$$, then $$I_{12}+I_{10}=$$
MHT CET 2023 14th May Morning Shift
The integral $$\int_\limits{\frac{\pi}{6}}^{\frac{\pi}{3}} \sec ^{\frac{2}{3}} x \operatorname{cosec}^{\frac{4}{3}} x d x$$ is equal to
MHT CET 2023 13th May Evening Shift
The integral $$\int_\limits{\pi / 6}^{\pi / 3} \sec ^{\frac{2}{3}} x \operatorname{cosec}^{\frac{4}{3}} x d x$$ is equal to
MHT CET 2023 13th May Morning Shift
If $$\mathrm{f}(x)=\left\{\begin{array}{ll}\mathrm{e}^{\cos x} \sin x & , \text { for }|x| \leq 2 \\ 2, & \text { otherwise }\end{array}\right.$$, the...
MHT CET 2023 12th May Evening Shift
The value of $$\int_\limits0^\pi\left|\sin x-\frac{2 x}{\pi}\right| \mathrm{d} x$$ is
MHT CET 2023 12th May Morning Shift
$$\int_\limits0^4|2 x-5| d x=$$
MHT CET 2023 11th May Evening Shift
Let $$f:[-1,2] \rightarrow[0, \infty)$$ be a continuous function such that $$\mathrm{f}(x)=\mathrm{f}(1-x), \forall x \in[-1,2]$$ Let $$\mathrm{R}_1=\... MHT CET 2023 11th May Morning Shift$$\int\limits_0^\pi \frac{d x}{4+3 \cos x}=$$MHT CET 2023 11th May Morning Shift Let$$\mathrm{f}(x)=\int \frac{\sqrt{x}}{(1+x)^2} \mathrm{~d} x, x \geq 0$$, then$$\mathrm{f}(3)-\mathrm{f}(1)$$is equal to MHT CET 2023 11th May Morning Shift Let$$\mathrm{f}(x)$$be positive for all real$$x$$. If$$\mathrm{I}_1=\int_\limits{1-\mathrm{h}}^{\mathrm{h}} x \mathrm{f}(x(1-x)) \mathrm{d} x$$an... MHT CET 2023 11th May Morning Shift$$\int_\limits{-1}^3\left(\cot ^{-1}\left(\frac{x}{x^2+1}\right)+\cot ^{-1}\left(\frac{x^2+1}{x}\right)\right) \mathrm{d} x=$$MHT CET 2023 10th May Evening Shift Let$$\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}$$and$$\mathrm{g}: \mathrm{R} \rightarrow \mathrm{R}$$be continuous functions. Then the value of... MHT CET 2023 10th May Evening Shift$$\int_\limits 0^\pi \frac{x \tan x}{\sec x+\cos x} d x= $$MHT CET 2023 10th May Evening Shift$$\int_\limits0^1 \cos ^{-1} x d x=$$MHT CET 2023 10th May Morning Shift If$$\int_\limits0^{\frac{1}{2}} \frac{x^2}{\left(1-x^2\right)^{\frac{3}{2}}} \mathrm{~d} x=\frac{\mathrm{k}}{6}$$, then the value of$$\mathrm{k}$$i... MHT CET 2023 9th May Evening Shift$$\int_\limits1^2 \frac{\mathrm{d} x}{\left(x^2-2 x+4\right)^{\frac{3}{2}}}=\frac{\mathrm{k}}{\mathrm{k}+5} \text {, then } \mathrm{k} \text { has the...
MHT CET 2023 9th May Morning Shift
If $$\mathrm{f}(x)$$ is a function satisfying $$\mathrm{f}^{\prime}(x)=\mathrm{f}(x)$$ with $$\mathrm{f}(0)=1$$ and $$\mathrm{g}(x)$$ is a function th...
MHT CET 2022 11th August Evening Shift
$$\int_\limits{\frac{\pi}{4}}^{\frac{3 \pi}{4}} \frac{\mathrm{d} x}{1+\cos x}$$ is equal to
MHT CET 2022 11th August Evening Shift
The value of the integral $$\int_\limits0^1 \sqrt{\frac{1-x}{1+x}} \mathrm{~d} x$$ is
MHT CET 2022 11th August Evening Shift
$$\int_\limits0^2[x] \mathrm{d} x+\int_\limits0^2|x-1| \mathrm{d} x=$$ (where $$[x]$$ denotes the greatest integer function.)
MHT CET 2021 24th September Evening Shift
$$\int_\limits2^5 2[\mathrm{x}] \mathrm{dx}=\{\text { where }[\mathrm{x}] \text { denotes the greatest integer function } \leq \mathrm{x}\}$$
MHT CET 2021 24th September Evening Shift
$$\int_\limits0^\pi x \sin x \cos ^4 x d x=$$
MHT CET 2021 24th September Morning Shift
$$\int_\limits0^4 x[x] d x=$$ (where $$[\mathrm{x}]$$ denotes greatest integer function not greater than $$\mathrm{x}]$$
MHT CET 2021 24th September Morning Shift
$$\int_\limits0^{\pi / 2} \log \left(\frac{4+3 \sin x}{4+3 \cos x}\right) d x=$$
MHT CET 2021 23rd September Evening Shift
$$\int_\limits0^\pi \frac{1}{4+3 \cos x} d x=$$
MHT CET 2021 23rd September Evening Shift
$$\int_\limits1^3\left[\tan ^{-1}\left(\frac{x}{x^2-1}\right)+\tan ^{-1}\left(\frac{x^2-1}{x}\right)\right] d x=$$
MHT CET 2021 23th September Morning Shift
$$\int_\limits0^1|5 x-3| d x=$$
MHT CET 2021 23th September Morning Shift
$$\int_0^{\pi / 2} \frac{\cos x}{3 \cos x+\sin x} d x=$$
MHT CET 2021 22th September Evening Shift
$$\int_\limits{\frac{\pi}{6}}^{\frac{\pi}{2}} \frac{\operatorname{cosec} x \cdot \cot x}{1+\operatorname{cosec}^2 x} d x=$$
MHT CET 2021 22th September Evening Shift
$$\int_\limits0^2|2 x-3| d x=$$
MHT CET 2021 22th September Evening Shift
If $$\int_\limits0^a \sqrt{\frac{a-x}{x}} d x=\frac{k}{2}$$, then $$k=$$
MHT CET 2021 22th September Morning Shift
$$\int\limits_{ - \pi }^\pi {{{x\sin x} \over {1 + {{\cos }^2}x}}dx = }$$
MHT CET 2021 22th September Morning Shift
The value of $$\int\limits_0^1 {{{\tan }^{ - 1}}\left( {{{2x - 1} \over {1 + x - {x^2}}}} \right)dx}$$ is
MHT CET 2021 21th September Evening Shift
$$\int\limits_5^{10} \frac{d x}{(x-1)(x-2)}=$$
MHT CET 2021 21th September Evening Shift
$$\int\limits_{{{ - \pi } \over 2}}^{{\pi \over 2}} {{{\cos x} \over {1 + {e^x}}}dx = }$$
MHT CET 2021 21th September Morning Shift
$$\int_\limits0^{\frac{\pi}{2}} \frac{\sin x-\cos x}{1-\sin x \cos x} d x=$$
MHT CET 2021 21th September Morning Shift
If $$f(x)=|x-1|+|x-2|+|x-3|, \forall x \in[1,4]$$, then $$\int_\limits1^4 f(x) d x=$$
MHT CET 2021 20th September Evening Shift
If $$2 f(x)-3 f\left(\frac{1}{x}\right)=x$$, then $$\int_\limits1^e f(x) d x=$$
MHT CET 2021 20th September Evening Shift
If $$\int_\limits2^e\left[\frac{1}{\log x}-\frac{1}{(\log x)^2}\right] d x=a+\frac{b}{\log 2}$$, then
MHT CET 2021 20th September Morning Shift
$$\int_\limits0^{\pi / 4} \log (1+\tan x) d x=$$
MHT CET 2021 20th September Morning Shift
If $$\int_\limits0^{\frac{\pi}{2}} \frac{d x}{5+4 \sin x}=A \tan ^{-1} B$$, then A + B =
MHT CET 2020 16th October Morning Shift
$$\int_0^a \sqrt{\frac{x}{a-x}} d x=$$
MHT CET 2020 16th October Morning Shift
$$\int_\limits2^3 \frac{x}{x^2-1} d x=$$
MHT CET 2020 16th October Morning Shift
$$\int_\limits0^{\frac{\pi}{2}} \log \left[\sqrt{\frac{1-\cos 2 x}{1+\cos 2 x}}\right] d x=$$
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