Mathematics

# Let $f(x)=\left\{\begin{matrix} x|x| & , & x\leq -1 \\ [x+1]+[1-x] & , & -1 < x < 1\\ -x|x| & , & x\geq 1\end{matrix}\right.$ (where $[\cdot]$ denotes the greatest integer function) then the value $\displaystyle\int^{2}_{-2}f(x)dx$, is equal to?

$-\dfrac{8}{3}$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

Q1 Subjective Medium
$\displaystyle \int a^{x}e^{x}dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Multiple Correct Hard
The integral $\displaystyle \int_{0}^{\pi} xf(\sin x)dx$ is equals to
• A. $\displaystyle \frac{\pi}{4}\int_{0}^{\pi} f(\sin x)dx$
• B. $\displaystyle \frac{\pi}{2}\int_{0}^{\pi} f(\sin x)dx$
• C. $\displaystyle \pi \int_{0}^{\pi/2} f(\sin x)dx$
• D. $\displaystyle \pi \int_{0}^{\pi/2} f(\cos x)dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
$\displaystyle \int \frac{\sin 2x+2\tan x}{\cos ^{6}x+6\cos ^{2}x+4}dx=$
• A. $\displaystyle 2\sqrt{\frac{1+\cos ^{2}x}{\cos ^{7}x}}$
• B. $\displaystyle \tan ^{-1}\frac{1}{\sqrt{2}}\left ( \frac{1+\cos ^{2}x}{\cos ^{7}x} \right )$
• C. none
• D. $\displaystyle \frac{1}{12}\log \left ( 1+\frac{6}{\cos ^{4}x}+\frac{4}{\cos ^{6}x} \right )$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate:
$\displaystyle\int\dfrac{x}{\sqrt{3x^2+4}}dx$.

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
Evaluate : $\displaystyle \int\frac {\sec\sqrt{x}.\tan\sqrt{x}}{\sqrt{x}}dx$
• A. $\sec\sqrt{x}+c$
• B. $\tan\sqrt{x}+c$
• C. $\displaystyle \frac{1}{2}\sec\sqrt{x}+c$
• D. $2\sec\sqrt{x}+c$