Mathematics

# $\int _{ -\frac { \pi }{ 2 } }^{ \frac { \pi }{ 2 } }{ \frac { { sin }^{ 2 }x }{ { 1+(2017) }^{ x } } dx }$ is

$\frac { \pi }{ 4 }$

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

#### Realted Questions

Q1 Subjective Hard
$\int\limits_0^{\frac{\pi }{2}} {\frac{{x\sin \,2x\,dx}}{{\cos 4x + \sin 4x}}}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evaluate $\displaystyle \int \dfrac{x}{x^2+3} dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
$\displaystyle\int \frac{1}{\sqrt{\left ( x^{2}+3x+1 \right )}}dx.$
• A. $\displaystyle \log \left [ \left ( x-3/2 \right ) \right ]+\sqrt{\left \{ \left ( x-3/2 \right )^{2}-\left ( \sqrt{3/2} \right )^{2} \right \}}.$
• B. $\displaystyle \log \left [ \left ( x+3/2 \right ) \right ]-\sqrt{\left \{ \left ( x+3/2 \right )^{2}-\left ( \sqrt{5/2} \right )^{2} \right \}}.$
• C. $\displaystyle \log \left [ \left ( x-3/2 \right ) \right ]-\sqrt{\left \{ \left ( x-3/2 \right )^{2}-\left ( \sqrt{3/2} \right )^{2} \right \}}.$
• D. $\displaystyle \log \left [ \left ( x+3/2 \right ) \right ]+\sqrt{\left \{ \left ( x+3/2 \right )^{2}-\left ( \sqrt{5/2} \right )^{2} \right \}}.$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Hard
Primitive of $\displaystyle \dfrac{3x^4-1}{(x^4+x+1)^2}$ w.r.t  $x$ is
• A. $\displaystyle \dfrac{x}{(x^4+x+1)}+c$
• B. $\displaystyle \dfrac{x+1}{(x^4+x+1)}+c$
• C. $-\displaystyle \dfrac{x+1}{(x^4+x+1)}+c$
• D. $-\displaystyle \dfrac{x}{(x^4+x+1)}+c$

$\int(2x^2-3 \, sin x+5 \sqrt{x})dx$