Mathematics

# $\displaystyle \int _{ 0 }^{ { \pi }^{ 2 } }{ \dfrac { \sin { \sqrt { x } } }{ \sqrt { x } } } dx$ is equal to

$2$

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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
The value of $\displaystyle\int _{ 0 }^{ \infty }{ \dfrac { dx }{ \left( { x }^{ 2 }+4 \right) \left( { x }^{ 2 }+9 \right) } }$ is
• A. $\dfrac { \pi }{ 20 }$
• B. $\dfrac { \pi }{ 40 }$
• C. $\dfrac { \pi }{ 80 }$
• D. $\dfrac { \pi }{ 60 }$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
Evaluate: $\displaystyle \int_{0}^{1}$ tan $^{-1}\left(\displaystyle \frac{3x-x^{3}}{1-3x^{2}}\right) dx$
• A. $\displaystyle \frac{3\pi}{2}-3\log 2$
• B. $\displaystyle \frac{7\pi}{2}+3\log 2$
• C. $\displaystyle \frac{3\pi}{4}+\frac{3}{2}|\mathrm{o}\mathrm{g}2$
• D. $\displaystyle \frac{3\pi}{4}-\frac{3}{2} \log 2$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate the following integrals :
$\displaystyle\int_{0}^{\pi} x\ dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Solve $\displaystyle\int { \dfrac { x }{ \sqrt { x+4 } } dx }$

Consider two differentiable functions $f(x), g(x)$ satisfying $\displaystyle 6\int f(x)g(x)dx=x^{6}+3x^{4}+3x^{2}+c$ & $\displaystyle 2 \int \frac {g(x)dx}{f(x)}=x^{2}+c$. where $\displaystyle f(x)>0 \forall x \in R$