Mathematics

Single Correct Medium Published on 17th 09, 2020
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Realted Questions

Q1 Single Correct Hard
$$\displaystyle \int {\frac{{dx}}{{(x + p)\sqrt {(x - p)(x - q)} }}} $$ is equal to 
  • A. $$\frac{2}{{p - q}}\sqrt {\frac{{x - p}}{{x - q}} + c} $$
  • B. $$ - \frac{2}{{p - q}}\sqrt {\frac{{x - q}}{{x - p}} + c} $$
  • C. None of these
  • D. $$\frac{1}{{\sqrt {\left( {x - p} \right)(x - q)} }} + c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q2 Single Correct Medium
Solve $$\displaystyle \int \sec(\log x)[1+\tan(\log x)]dx$$
  • A. $$\displaystyle \frac{x}{2}\sec(\log x)+c$$
  • B. $$\displaystyle -x\sec(\log x)+c$$
  • C. $$\displaystyle \frac{-x}{2} \sec(\log x)+c$$
  • D. $$\displaystyle x\sec(\log x)+c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q3 Subjective Hard
$$\int {\frac{{{e^x}}}{x}\,\left( {1 + x.lnx} \right)} \,dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q4 Subjective Medium
Evaluate the following integral:
$$\displaystyle\int^{\pi/2}_0\dfrac{\sin x}{\sqrt{1+\cos x}}dx$$.

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q5 Single Correct Medium
$$\displaystyle \int_1^{32}\dfrac{dx}{x^{1/5}\sqrt{1+x^{4/5}}}$$
  • A. $$\dfrac{2}{5}(\sqrt{17}-\sqrt{2})$$
  • B. $$\dfrac{5}{2}(\sqrt{17}-\sqrt{2})$$
  • C. $$\dfrac{5}{2}(\sqrt{17}+\sqrt{2})$$
  • D. $$\dfrac{2}{5}(\sqrt{17}+\sqrt{2})$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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