Mathematics

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


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Subjective Medium Published on 17th 09, 2020
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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. $$\dfrac{1}{3} \left(e^2 - \dfrac{1}{e} \right)$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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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 $$\displaystyle \left ( 0,2 \right )$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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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. $$x+c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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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. $$\displaystyle \sin^{-1}\left ( \frac{ax+\frac{b}{x}}{c} \right )+k$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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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. $$\sin x-2(\sin x)^{-1}-6\tan^{-1}(\sin x)+c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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