Mathematics

# Evaluate the given integral: $\displaystyle \int_{0}^{4} {(4x-x^2)}dx$

##### SOLUTION

Consider, $I=\displaystyle \int_{0}^{4} {(4x-x^2)}dx$

$I=\left[ 2x^2-\dfrac{x^3}3 \right]_0^4$

$I=32-\dfrac{64}3$

$I =\dfrac {32}3$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

Q1 Single Correct Medium
$\displaystyle \int \dfrac{x-\sin{x}}{1-\cos{c}}dx$
• A. $-x\cot{\dfrac{x}{2}}+c$
• B. $\cot{\dfrac{x}{2}}+c$
• C. $None \ of\ these$
• D. $x\cot{\dfrac{x}{2}}+c$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
$\displaystyle \int x.\sqrt{\left [ \frac{2\sin \left ( x^{2}-1 \right )-\sin 2\left ( x^{2}-1 \right )}{2\sin \left ( x^{2}-1 \right )+\sin 2\left ( x^{2}-1 \right )} \right ]}dx$ where $\displaystyle x^{2}-1\neq n\pi$
• A. $\displaystyle \log \sec {x^{2}-1}.$
• B. $\displaystyle \log \tan \frac{x^{2}-1}{2}.$
• C. $\displaystyle \log \cos \frac{x^{2}-1}{2}.$
• D. $\displaystyle \log \sec \frac{x^{2}-1}{2}.$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
$\displaystyle\int\limits_{a}^{b}f(x)\ dx=b^3-a^3$, then find $f(x)$.

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Hard
lf $f(x)=\displaystyle \frac{x+2}{2x+3}$ , then $\displaystyle \int(\frac{f(x)}{x^{2}})^{1/2}dx$ is

equal to
$\displaystyle \frac{1}{\sqrt{2}}g(\frac{1+\sqrt{2f(x)}}{1-\sqrt{2f(x)}})-\sqrt{\frac{2}{3}}h(\frac{\sqrt{3f(x)}+\sqrt{2}}{\sqrt{3f(x)}-\sqrt{2}})+c$
where
• A. $g(x)=\tan^{-1}x,\ h(x)=\log|x|$
• B. $g(x)=\log|x|,h(x)=\tan^{-1}x$
• C. $g(x)=h(x)=\tan^{-1}x$
• D. $g(x)=\log|x|, h(x)=\log|x|$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
If $I=\displaystyle \int^{e}_{\dfrac {1}{e}}|\log|.\dfrac {dx}{x^{2}}$ then  $I=$
• A. $\dfrac {2}{e}$
• B. $2\left(1-\dfrac {1}{e}\right)$
• C. $0$
• D. $2$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020