Mathematics

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

Q1 Single Correct Medium
Solve $$\displaystyle\int {\dfrac{{dx}}{{\sqrt {x - {x^2}} }}} $$
  • A. $$ I={{\sin }^{-1}}\left( 2x+1 \right)+C $$
  • B. $$ I={{\sin }^{-1}}\left( x-1 \right)+C $$
  • C. None of these
  • D. $$ I={{\sin }^{-1}}\left( 2x-1 \right)+C $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q2 Subjective Medium
Integrate:$$\displaystyle \int _{ 0 }^{ \pi /2 }{ \cos ^{ 2 }{ x } dx } $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q3 Single Correct Medium
Solve $$\displaystyle\int \dfrac {\tan x}{(a^{2} + b^{2}\tan^{2}x)} dx$$.
  • A. $$I= \dfrac{1}{{5\left( {{b^2} - {a^2}} \right)}}\log \left| {{a^2}{{\cos }^2}x + {b^2}{{\sin }^2}x} \right| + C$$
  • B. $$I= \dfrac{1}{{2\left( {{b^2} - {a^2}} \right)}}\log \left| {{a^2}{{\cos }^2}x - {b^2}{{\sin }^2}x} \right| + C$$
  • C. None of these
  • D. $$I= \dfrac{1}{{2\left( {{b^2} - {a^2}} \right)}}\log \left| {{a^2}{{\cos }^2}x + {b^2}{{\sin }^2}x} \right| + C$$

Asked in: Mathematics - Integrals


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Q4 Subjective Hard
Evaluate : $$\displaystyle \int \dfrac{\sin^{8} x- \cos^{8} x}{1-2 \sin^{2} x \cos^{2} x} dx$$

Asked in: Mathematics - Integrals


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Q5 Subjective Medium
Solve $$\displaystyle\int\dfrac{{{{\left( {\log \,x} \right)}^2}}}{x}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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