Mathematics

Single Correct Medium Published on 17th 09, 2020
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Q1 Single Correct Medium
$$\displaystyle \int {\cos 2\theta \,\log \left( {\frac{{\cos \theta  + \sin \theta }}{{\cos \theta  - \sin \theta }}} \right)} d\theta $$ is equal to.
  • A. $${(\cos \theta + \sin \theta )^2}\log \left( {\frac{{\cos \theta + \sin \theta }}{{\cos \theta - \sin \theta }}} \right) + C$$
  • B. $$\frac{{{{(\cos \theta - \sin \theta )}^2}}}{2}\log \left( {\frac{{\cos \theta + \sin \theta }}{{\cos \theta - \sin \theta }}} \right) + C$$
  • C. None of these
  • D. $${(\cos \theta - \sin \theta )^2}\log \left( {\frac{{\cos \theta + \sin \theta }}{{\cos \theta - \sin \theta }}} \right) + C$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q2 Single Correct Medium
$$\displaystyle \int_{0}^{\pi /2}\frac{dx}{\sin x}$$equals
  • A. $$\displaystyle \frac{1}{2}$$
  • B. $$1$$
  • C. $$3/2$$
  • D. $$0$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q3 Subjective Medium
$$\displaystyle \int \dfrac{1}{3x^{2}+x}dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q4 Single Correct Medium
$$\displaystyle \int\frac{4\sec^{2}x\tan x}{\sec^{2}x+\tan^{2}x}dx=$$
  • A. $$ 2\log(\sec^{2}x+\tan^{2}x)+c$$
  • B. $$ \log(2x+\tan^{2}x)+c$$
  • C. $$ 2\tan^{2}x+c$$
  • D. $$ \log (\sec^{2}x+\tan^{2}x) +c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q5 Subjective Easy
$$\int(2x^2-3 \, sin x+5 \sqrt{x})dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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