Mathematics

# $\int { x\left( \dfrac { \sec { 2x } -1 }{ \sec { 2x } +1 } \right) dx }$

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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

$\displaystyle \int_{0}^{\pi /2}x^{2}.\sin x dx=$
• A. 2 $\pi$
• B. $\pi/2$
• C. $\pi+1$
• D. $\pi-2$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
If $f(x)=\dfrac{\sin x}{x} \forall x \in(0, \pi],$ prove that$\dfrac{\pi}{2} \int_{0}^{\pi / 2} f(x) f\left(\dfrac{\pi}{2}-x\right) d x=\int_{0}^{\pi} f(x) d x$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
Evaluate $\displaystyle \int\frac{\log(x/e)}{(\log x)^{2}}dx$
• A. $\displaystyle \frac{\log x}{x}+c$
• B. $^{\dfrac{x}{log(x)^{2}}+c}$
• C. $\displaystyle \frac{(\log x)^{2}}{x}+c$
• D. $\displaystyle \frac{x}{\log x}+c$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium

Evaluate $\displaystyle \int x\frac{(\sec 2x-1)}{(\sec 2x+1)}dx$
• A. $x \tan x-\log |\displaystyle \sec x|+\frac{x^{2}}{2}+c$
• B. $x \tan x-\log |\sec\frac{x}{2}|+c$
• C. $x \tan x-\log |\displaystyle \sec\frac{x}{2}|+\frac{x^{2}}{2}+c$
• D. $x \tan x-\log |\displaystyle \sec x|-\frac{x^{2}}{2}+c$

Consider the integrals $I_1=\int_{\frac{\pi}{6}}^{\frac{\pi}{3}}\frac{dx}{1+\sqrt{tan x}}$ and $I_2=\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{\sqrt{sin x}dx}{\sqrt{sin }x+\sqrt{cos}x}$