Mathematics

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

Q1 Single Correct Hard
If $$\displaystyle I = \int \frac {dx}{(2 \sin x + \sec x)^4}$$, then I equals
  • A. $$\displaystyle \frac {1}{5 \tan^5 x} + \frac {1}{3 \tan^6 x} - \frac {I}{(2 \sin x + \sec x)^3} + C$$
  • B. $$\displaystyle \frac {-1}{3(2 \sin x + \sec)^3} + \tan^{-1} (3\sqrt {\tan x}) + C$$
  • C. $$\displaystyle \frac {-1}{3(2 \sin x + \sec x)^3} - \tan^{-1} (3\sqrt {\tan x}) + C$$
  • D. $$\displaystyle -\frac {1}{5 \tan^5 x} + \frac {1}{3 \tan^6 x} - \frac {2}{7 \tan^7 x} + C$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q2 Subjective Medium
Solve:
$$\int \ \sqrt{x^{2}+4x+1} \ dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q3 Single Correct Hard
Let $$f(x)$$ be a positive function. Let
$$I_{1} = \int_{1 - k}^{k} xf\left \{x(1 - x)\right \} dx$$,
$$I_{2} = \int_{1 - k}^{k} f\left \{x(1 - x) \right \} dx$$,
where $$2k - 1 > 0$$, then $$\dfrac {I_{1}}{I_{2}}$$ is
  • A. $$2$$
  • B. $$k$$
  • C. $$1$$
  • D. $$\dfrac {1}{2}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q4 Subjective Hard
$$\displaystyle \int \cos^{-1} \left( \frac { 1- \tan^2 x}{1+ \tan^2 x } \right) dx $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q5 Single Correct Medium
$$\displaystyle  \int\frac{d{x}}{4\sin^2{x}+4\sin{x}\cos x+5\cos^{2}x}=$$
  • A. $$\tan^{-1} (2\tan x+1)+c$$
  • B. $$\tan^{-1}(\displaystyle \tan x+\frac{1}{2})+c$$
  • C. $$\displaystyle \frac{1}{4}\tan (2\tan x+1)+c$$
  • D. $$\displaystyle \frac{1}{8}\tan^{-1} (\tan x+\displaystyle \frac{1}{2})+c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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