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Realted Questions

Q1 Single Correct Hard
Evaluate : $$\displaystyle\int _{ \tfrac{ \pi  }{ 6 } }^{ \tfrac{ \pi  }{ 3 } }{ \dfrac { dx }{ 1+\sqrt { \tan { x }  }  }  } $$
  • A. $$\dfrac{\pi}{4}$$
  • B. $$\dfrac{\pi}{8}$$
  • C. $$\dfrac{\pi}{6}$$
  • D. $$\dfrac{\pi}{12}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q2 Single Correct Hard
If $$\displaystyle I = \int \left ( \sqrt {\frac {a + x}{a - x}} + \sqrt {\frac {a - x}{a + x}} \right ) dx$$, then I equals
  • A. $$\displaystyle 2 \sin^{-1} \left ( \frac {x}{a} \right ) + C$$
  • B. $$\displaystyle 2 \cos^{-1} \left ( \frac {x}{a} \right ) + C$$
  • C. $$\displaystyle 2a \cos^{-1} \left ( \frac {x}{a} \right ) + C$$
  • D. $$\displaystyle 2a \sin^{-1} \left ( \frac {x}{a} \right ) + C$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q3 Single Correct Medium
$$\int (1- \cos x)\ \text{cosec}^2x \;dx  = f(x) +c\; implies\; f(x) = $$
  • A. $$\cot \dfrac{x}{2}$$+C
  • B. $$2\tan \dfrac{x}{2}$$+C
  • C. $$\dfrac{1}{2} \ tan \dfrac{x}{2}$$+C
  • D. $$\tan \dfrac{x}{2}$$+C

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q4 Subjective Medium
$$\int {{{\sin }^{ - 1}}dx} $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q5 Subjective Medium
Evaluate: $$\displaystyle\int\displaystyle\frac{x^3+5x^2+4x+1}{x^2}dx$$.

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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