Mathematics

# Solve:$\displaystyle\int_{0}^{3}|3x-1|\ dx$

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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
Evaluate : $\underset{0}{\overset{1}{\int}} e^{2 - 3x} dx$
• A. $e^2 - e$
• B. $\dfrac{1}{3} (e^2 - e)$
• C. $\dfrac{1}{2} \left(e^2 - \dfrac{1}{e} \right)$
• D. $\dfrac{1}{3} \left(e^2 - \dfrac{1}{e} \right)$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
Let a, b, c be non-zero real numbers such the : $\displaystyle \int_{0}^{1}\left ( 1+\cos ^{8}x \right )\left ( ax^{2}+bx+c \right )dx=\int_{0}^{2}\left ( 1+\cos ^{8}x \right )\left ( ax^{2}+bx+c \right )dx,$ then the quadratic equation $\displaystyle ax^{2}+bx+c=0$ has
• A. no root in $\displaystyle \left ( 0,2 \right )$
• B. a double root in $\displaystyle \left ( 0,2 \right )$
• C. none
• D. atleast one root in $\displaystyle \left ( 0,2 \right )$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
Let $f\left( x \right)$ be a polynomial of degree three satisfying $f\left( 0 \right) =-1$ and $f(1)=0$. Also, $0$ is a stationary point of $f(x)$. If $f(x)$ does not have an extremum at $x=0$, then $\displaystyle \int { \frac { f\left( x \right) }{ { x }^{ 3 }-1 } dx }$ is equal to
• A. $\displaystyle \frac { { x }^{ 2 } }{ 2 } +c$
• B. $\displaystyle \frac { { x }^{ 3 } }{ 6 } +c$
• C. None of these
• D. $x+c$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Hard
The value of $\displaystyle \int \frac{(ax^{2}-b)dx}{x\sqrt{c^{2}x^{2}-(ax^{2}+b)^{2}}}$ is equal to
• A. $\displaystyle \frac{1}{c}\sin^{-1}\left ( ax+\frac{b}{x} \right )+k$
• B. $\displaystyle c\sin^{-1}\left ( a+\frac{b}{x} \right )+k$
• C. none of these
• D. $\displaystyle \sin^{-1}\left ( \frac{ax+\frac{b}{x}}{c} \right )+k$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
The value of the integral $\displaystyle\int\dfrac{\cos^{3}x+\cos^{5}x}{\sin^{2}x+\sin^{4}x}dx$ is
• A. $\sin x-6\tan^{-1}(\sin x)+c$
• B. $\sin x-2(\sin x)^{-1}+c$
• C. $\sin x-2(\sin x)^{-1}+5\tan^{-1}(\sin x)+c$
• D. $\sin x-2(\sin x)^{-1}-6\tan^{-1}(\sin x)+c$