Mathematics

# $\int^2_0 (\sqrt{\dfrac{4-x}{x}} - \sqrt{\dfrac{x}{4-x}})dx$ is equal to

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

#### Realted Questions

Q1 Single Correct Hard
$\displaystyle\int{\frac{1}{(x+1)\sqrt{2+x-x^2}}dx}$ is equal to
• A. $\displaystyle \frac{2}{3}\sqrt{3\left(\frac{1}{x-1}\right)-1}+C$
• B. $\displaystyle \frac{3}{2}\sqrt{3\left(\frac{1}{x-1}\right)-1}+C$
• C. $\displaystyle-\frac{4}{3}\sqrt{3\left(\frac{1}{x-1}\right)-1}+C$
• D. $\displaystyle-\frac{2}{3}\sqrt{3\left(\frac{1}{x+1}\right)-1}+C$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
A tank initially holds 10 lit. of fresh water. At t = 0, a brine solution containing $\displaystyle \frac{1}{2}$ kg of salt per lit. is poured into tank at a rate 1 lit/min while the well-stirred mixture leaves the tank at the same rate. Find the amount of salt in a tank at a particular time
• A. $5e^{-t} + 5$
• B. $5e^{-t} - 5$
• C. $-5e^{} - 5$
• D. $- 5e^{-t} + 5$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate the following : $\int _{ -\frac { \pi }{ 4 } }^{ \frac { \pi }{ 4 } }{ \dfrac { x+\dfrac { \pi }{ 4 } }{ 2-\cos 2x } dx }$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Hard
Solve : $\int { \dfrac { cos4\theta +1 }{ cot\theta -tan\theta } d\theta }$

Solve $\displaystyle\int \dfrac{x}{{{{\left( {x + 1} \right)}^2}}}dx$