Mathematics

$\displaystyle \int_{\pi/4}^{\pi/2}{\sqrt{2+\sqrt{2+2\cos 4x}}dx}$ is equal to

$\sqrt{2}$

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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 Medium
$\int_{}^{} {x{{\sin }^{ - 1}}xdx}$
• A. $\frac{1}{4}{\sin ^{ - 1}}x\left( {2x + 1} \right) + \frac{{x\sqrt {1 - {x^2}} }}{4} + c$
• B. $\frac{1}{4}{\cos ^{ - 1}}x\left( {2x + 1} \right) + \frac{{x\sqrt {1 - {x^2}} }}{4} + c$
• C. $\frac{1}{4}{\sin ^{ - 1}}x\left( {2x + 1} \right) - \frac{{x\sqrt {1 - {x^2}} }}{4} + c$
• D. $\frac{1}{4}{\sin ^{ - 1}}x\left( {2{x^2} + 1} \right) + \frac{{x\sqrt {1 - {x^2}} }}{4} + c]$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle \int_{1}^{e}\log x \,dx =$________
• A. $e + 1$
• B. $e -1$
• C. $e + 2$
• D. $1$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium

$\displaystyle \int_{0}^{\pi /2}\log(\tan x+\cot x)dx=$
• A. $-\pi$ log2
• B. $-\displaystyle \frac{\pi}{2}$ log2
• C. $\displaystyle \frac{\pi}{2}$ log2
• D. $\pi$ log2

1 Verified Answer | Published on 17th 09, 2020

Q4 Multiple Correct Hard
$\displaystyle \int _{ \alpha }^{ \beta } \sqrt { \frac { x-\alpha }{ \beta -x } } dx=$
• A. $\displaystyle \frac{\pi^{2}}{2}(\beta-\alpha)$
• B. $\displaystyle \int_{\alpha}{\beta}\sqrt{\frac{\beta+x}{x+\alpha}}dx$
• C. $\displaystyle \int_{\alpha}{\beta}\sqrt{\frac{\beta-x}{x-\alpha}}dx$
• D. $\displaystyle \frac{\pi}{2}(\beta-\alpha)$

Find the value of $\displaystyle\int\limits_{-\dfrac{\pi}{2}}^{\dfrac{\pi}{2}}|\sin x|\ dx$.