Mathematics

# Evaluate:$\displaystyle \int _{ 0 }^{ \sqrt { 2 } }{ { x }^{ 2 } } dx$

$\dfrac{2\sqrt{2}}{3}$

##### SOLUTION
Given,

$\displaystyle \int _0^{\sqrt{2}}x^2dx$

$=\left .\dfrac{x^{2+1}}{2+1}\right|^{\sqrt{2}}_0$

$=\left.\dfrac{x^3}{3}\right|^{\sqrt{2}}_0$

$=\dfrac{2\sqrt{2}}{3}$

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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 Hard
If $\mathrm{a}>\mathrm{b}$ then $\displaystyle \int_{0}^{\pi}\frac{\mathrm{d}\mathrm{x}}{\mathrm{a}+\mathrm{b}\sin \mathrm{x}}=$
• A. $\displaystyle \frac{1}{\sqrt{\mathrm{a}^{2}-\mathrm{b}^{2}}}\cot^{-1}(\frac{\mathrm{b}}{\sqrt{\mathrm{a}^{2}-\mathrm{b}^{2}}})$
• B. $\displaystyle \frac{1}{\sqrt{\mathrm{a}^{2}-\mathrm{b}^{2}}}\tan^{-1}(\frac{\mathrm{b}}{\sqrt{\mathrm{a}^{2}-\mathrm{b}^{2}}})$
• C. $\displaystyle \frac{2}{\sqrt{\mathrm{a}^{2}-\mathrm{b}^{2}}}\tan^{-1}(\frac{\mathrm{b}}{\sqrt{\mathrm{a}^{2}-\mathrm{b}^{2}}})$
• D. $\displaystyle \frac{2}{\sqrt{\mathrm{a}^{2}-\mathrm{b}^{2}}}\cot^{-1}(\frac{\mathrm{b}}{\sqrt{\mathrm{a}^{2}-\mathrm{b}^{2}}})$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evaluate the following integral:
$\displaystyle \int { \cfrac { \left( x+1 \right) { e }^{ x } }{ \cos ^{ 2 }{ \left( x{ e }^{ x } \right) } } } dx\quad$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Solve:
$\int {\sin ^4}x$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
$\displaystyle \int_{-\pi/2}^{\pi/2} \tan x^3dx=$ ?
• A. $1$
• B. $\dfrac{1}{2}$
• C. $2$
• D. $0$

$\int 2^{2^{2^{x}}} 2^{2^{x}} 2^{x}dx$.