Mathematics

# $\int^{7}_{3}\sqrt {\dfrac {7-x}{x-3}}dx$

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

#### Realted Questions

Q1 Single Correct Medium
The value of $\displaystyle \int_{0}^{1}\displaystyle \frac{dx}{\left ( x+1 \right )\sqrt{x^{2}+2x}}$ is
• A. $\pi /6$
• B. $\pi /2$
• C. $\pi$
• D. $\pi /3$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\int\displaystyle\frac{x^2+1}{x^4+1}dx$ is equal to.
• A. $\displaystyle\frac{1}{\sqrt 2}\tan^{-1}\left(\displaystyle\frac{x^2}{\sqrt 2 x}\right)+c$
• B. $\displaystyle\frac{1}{\sqrt 2}\tan^{-1}\left(\displaystyle\frac{x^2+1}{x}\right)+c$
• C. $\displaystyle\tan^{-1}\left(\displaystyle\frac{x^2-1}{\sqrt 2 x}\right)+c$
• D. $\displaystyle\frac{1}{\sqrt 2}\tan^{-1}\left(\displaystyle\frac{x^2-1}{\sqrt 2 x}\right)+c$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
Evaluate $\int x^{3}\, \sin(x^{2}) dx$
• A. $-\displaystyle\frac { 1 }{ 2 } \left( \sin { \left( { x }^{ 2 } \right) -{ x }^{ 2 }\cos { \left( { x }^{ 2 } \right) } } \right) +c$
• B. $\displaystyle\frac { 1 }{ 2 } \left( \sin { \left( { x }^{ 2 } \right) +{ x }^{ 2 }\cos { \left( { x }^{ 2 } \right) } } \right) +c$
• C. $\displaystyle \frac{1}{2}\, x^{2}\, \cos(x^{2}) + \sin(x^{2}) + c$
• D. $\displaystyle\frac { 1 }{ 2 } \left( \sin { \left( { x }^{ 2 } \right) -{ x }^{ 2 }\cos { \left( { x }^{ 2 } \right) } } \right) +c$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate: $\displaystyle \int _{\pi/6}^{\pi/3}\dfrac{\sin{x}+\cos{x}}{\sqrt{\sin{2x}}}dx$

Let $\displaystyle f\left ( x \right )=\frac{\sin 2x \cdot \sin \left ( \dfrac{\pi }{2}\cos x \right )}{2x-\pi }$