Mathematics

# The value of the define integral $\int_{\frac{3}{2}}^{\frac{9}{4}}[\sqrt{2x-\sqrt{5(4x-5)}}+\sqrt{2x+\sqrt{5(4x-5)}}]dx$ is equal to

$4\sqrt{5}-\frac{2\sqrt{2}}{5}$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### Realted Questions

Q1 Single Correct Hard
The integral $\int_{\pi /4}^{\pi / 2}(2cosec x)^{17}dx$ is equal to
• A. $\int_{0}^{\log(1 + \sqrt {2})} 2(e^{u} + e^{-u})^{17}du$
• B. $\int_{0}^{\log(1 + \sqrt {2})} 2(e^{u} - e^{-u})^{17}du$
• C. $\int_{0}^{\log(1 + \sqrt {2})} 2(e^{u} - e^{-u})^{16}du$
• D. $\int_{0}^{\log(1 + \sqrt {2})} 2(e^{u} + e^{-u})^{16}du$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
Let $f(0) = 0$ and $\displaystyle \int_{0}^{2}{f}'(2t)e^{f(2t)} \:dt=5$.
Then the value of $f (4)$ is?
• A. $\log 2$
• B. $\log 7$
• C. $\log 13$
• D. $\log 11$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
$\displaystyle \frac{3\mathrm{x}^{2}+1}{(\mathrm{x}^{2}+1)^{3}}=\frac{\mathrm{A}\mathrm{x}+\mathrm{B}}{(\mathrm{x}^{2}+1)}+\frac{\mathrm{C}\mathrm{x}+\mathrm{D}}{(\mathrm{x}^{2}+1)^{2}}+\frac{\mathrm{E}\mathrm{x}+\mathrm{F}}{(\mathrm{x}^{2}+1)^{3}}$ then $A + C + E + F =$
• A. 10
• B. -10
• C. 2
• D. -2

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
$\displaystyle\int \frac{x^{3}}{25x^{8}-16}dx.$
• A. $\displaystyle \frac{1}{160}\log \frac{5x^{4}+4}{5x^{4}-4}$
• B. $\displaystyle \frac{1}{80}\log \frac{5x^{4}-4}{5x^{4}+4}$
• C. $\displaystyle \frac{1}{40}\log \frac{5x^{4}+4}{5x^{4}-4}$
• D. $\displaystyle \frac{1}{160}\log \frac{5x^{4}-4}{5x^{4}+4}$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
$\displaystyle \overset{1}{\underset{-1}{\int}} x|x|dx$ is equal to
• A. $\dfrac{2}{3}$
• B. $-\dfrac{2}{3}$
• C. None of these
• D. $0$