Mathematics

# Evaluate $\displaystyle\int_{0}^{2}(x+1)\ dx$

##### SOLUTION
Consider, $I=\displaystyle\int_{0}^{2}x+1\ dx$

$=\left[\dfrac {x^2}2 +x \right]_0^2$

$=2+2=4$

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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

$\displaystyle \int_{1}^{2}\frac{\mathrm{d}\mathrm{x}}{\sqrt{1+\mathrm{x}^{2}}}=$
• A. $\displaystyle \log_{\mathrm{e}}(\frac{\sqrt{2}+1}{2+\sqrt{5}})$
• B. $\displaystyle \log_{\mathrm{e}}(\frac{2-\sqrt{5}}{\sqrt{2}-1})$
• C.
• D. $\displaystyle \log_{\mathrm{e}}(\frac{2+\sqrt{5}}{\sqrt{2}+1})$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
Evaluate : $\displaystyle \int \sqrt{\dfrac{a - x}{x}} dx$
• A. $\dfrac{\sqrt{a-x}}{\sqrt{x}}+a\tan^{-1}\left(\dfrac{\sqrt{x}}{\sqrt{a-x}}\right)+c$
• B. $\dfrac{\sqrt{a-x}}{\sqrt{x}}-a\tan^{-1}\left(\dfrac{\sqrt{x}}{\sqrt{a-x}}\right)+c$
• C. $\sqrt{a-x} \sqrt{x}-a\tan^{-1}\left(\dfrac{\sqrt{x}}{\sqrt{a-x}}\right)+c$
• D. $\sqrt{a-x} \sqrt{x}+a\tan^{-1}\left(\dfrac{\sqrt{x}}{\sqrt{a-x}}\right)+c$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
$\displaystyle \int_1^{\sqrt 3}\frac {dx}{1+x^2}$ equals
• A. $\dfrac {\pi}{3}$
• B. $\dfrac {2\pi}{3}$
• C. $\dfrac {\pi}{6}$
• D. $\dfrac {\pi}{12}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
Let $a,\ b,\ c$ be such that $\displaystyle \frac{1}{(1-x)(1-2x)(1-3x)}=\frac{a}{1-x}+\frac{b}{1-2x}+\frac{c}{1-3x}$ then $\displaystyle \frac{a}{1}+\frac{b}{3}+\frac{c}{5}=$
• A. $\displaystyle \frac{1}{6}$
• B. $\displaystyle \frac{1}{5}$
• C. $\displaystyle \frac{1}{3}$
• D. $\displaystyle \frac{1}{15}$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
$4 \displaystyle \int \dfrac{\sqrt{a^6 + x^8}}{x} dx$ is equal to ______________________.
• A. $a^6 ln\vert \dfrac {\sqrt{a^6 + x^8} - a^3} {\sqrt {a^6 + x^8} + a^3}\vert + c$
• B. $\sqrt{a^6 + x^8} + \dfrac {a^3}{2} ln \vert \dfrac {\sqrt{a^6 + x^8} - a^3} {\sqrt {a^6 + x^8} + a^3}\vert + c$
• C. $a^6 ln \vert \dfrac {\sqrt{a^6 + x^8} + a^3} {\sqrt {a^6 + x^8} - a^3}\vert + c$
• D. $\sqrt{a^6 + x^8} + \dfrac{a^3}{2} ln \vert \dfrac {\sqrt{a^6 + x^8} + a^3} {\sqrt {a^6 + x^8} - a^3}\vert + c$