Mathematics

# The value of integral $\underset{0}{\overset{50 \pi}{\int}} \sqrt{1 + cos 2x} dx$ is

$50 \sqrt{2}$

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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 Medium
$n\overset{Lt}{\rightarrow}\infty \displaystyle \{\frac{1}{n+1}+\frac{1}{n+2}+\ldots+\frac{1}{6n}\}=$
• A. log 2
• B. log 3
• C. log 5
• D. log 6

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
If $\displaystyle f(x)=\lim_{n\rightarrow \infty }(2x+4x^{3}+......+2^{n}x^{2n-1})\left ( 0<x<\frac{1}{\sqrt{2}} \right )$, then the value of $\displaystyle\int f(x) dx$ is equal to
$\textbf{Note}$: $c$ is the constant of integration.
• A. $\displaystyle \log\left ( \frac{1}{\sqrt{1-x^{2}}} \right )+c$
• B. $\displaystyle \log\sqrt{1-2x^{2}+x} + c$
• C. None of these
• D. $\displaystyle \log\left ( \frac{1}{\sqrt{1-2x^{2}}} \right )+c$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
$\dfrac{3x+7}{x^{2}-3x+2}=$
• A. $\displaystyle \frac{5}{x-1}+\frac{8}{x-2}$
• B. $\displaystyle \frac{8}{x-1}+\frac{5}{x-2}$
• C. $\displaystyle \frac{2}{x-1}+\frac{3}{x-2}$
• D. $\displaystyle \frac{13}{x-2}-\frac{10}{x-1}$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
$\displaystyle \int \frac{1}{\sqrt{\left ( x \right )}\left [ \sqrt{\left ( x \right )}+1 \right ]}dx.$
• A. $\displaystyle 2\log \left ( 1-\sqrt{x} \right ).$
• B. $\displaystyle \log \left ( 1+\sqrt{x} \right ).$
• C. $\displaystyle \sqrt{2}\log \left ( 1+\sqrt{x} \right ).$
• D. $\displaystyle 2\log \left ( 1+\sqrt{x} \right ).$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Hard
Evaluate $\displaystyle I_1=\int_0^{\displaystyle\frac{\pi}{2}}{\cos{(\pi\sin^2{x})}dx}$ $\displaystyle$
• A. $\pi$
• B. $\dfrac{\pi}{2}$
• C. none of the above.
• D. $0$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020