Mathematics

Single Correct Medium Published on 17th 09, 2020
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Q1 Single Correct Medium
The value of $$\int_{0}^{1} \dfrac {8\log (1 + x)}{1 + x^{2}} dx$$ is
  • A. $$2\pi \log 2$$
  • B. $$ \log 2$$
  • C. None of these
  • D. $$\pi \log 2$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q2 Single Correct Medium
$$\displaystyle \int_{-1}^{1} \dfrac{x^3 + |x| + 1}{x^2 + 2|x| + 1} dx$$ is equal to
  • A. $$log \,2$$
  • B. $$\dfrac{1}{2} \,log \,2$$
  • C. $$4 \,log \,2$$
  • D. $$2 \,log \,2$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q3 Single Correct Medium
If $$\dfrac{3\mathrm{x}+4}{\mathrm{x}^{2}-3\mathrm{x}+2}=\dfrac{\mathrm{A}}{\mathrm{x}-2}+\dfrac{\mathrm{B}}{\mathrm{x}-1}$$ then $$(A,B)=$$
  • A. (7, 10)
  • B. (10, 7)
  • C. (-10, 7)
  • D. (10, -7)

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q4 Single Correct Hard
$$\displaystyle \int \frac{\mathrm{cosec} ^{2}x-2005}{\cos ^{2005}x}dx$$ is equal to
  • A. $$\displaystyle \frac{\cot x}{(\cos x)^{2005}}+c$$
  • B. $$\displaystyle \frac{\tan x}{(\cos x)^{2005}}+c$$
  • C. $$\displaystyle \frac{(-\tan x)}{(\cos x)^{2005}}+c$$
  • D. none of these

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q5 Subjective Easy
Evaluate:
$$ \int_{}^{} {\frac{{ - 1}}{{\sqrt {1 - {x^2}} }}dx} $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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