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Realted Questions

Q1 Subjective Hard
Evaluate: $$\int\,sin 2 x.cos^{11/2}\,x.(1+cos^{5/2}\,x)^{1/2} dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q2 Single Correct Hard
The value of $$\displaystyle \int\limits_0^1 {\dfrac{{x{{\tan }^{ - 1}}x}}{{{{\left( {1 + {x^2}} \right)}^{3/2}}}}} dx$$ is 
  • A. $$\dfrac{{4 + \pi }}{{4\sqrt 2 }}$$
  • B. $$\dfrac{\pi }{2}$$
  • C. $$ - \dfrac{\pi }{2}$$
  • D. $$\dfrac{{4 - \pi }}{{4\sqrt 2 }}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q3 Single Correct Hard
$$\displaystyle \int \sqrt{x}(1+x^{1/3})^{4}dx$$ is equal to
  • A. $$\displaystyle 2\left \{ x^{3/2}+\frac{4}{11}x^{11/6}+\frac{6}{13}x^{13/6}+\frac{4}{15}x^{5/2}+\frac{1}{17}x^{17/6} \right \}+c$$
  • B. $$\displaystyle 6\left \{ x^{3/2}-\frac{4}{11}x^{11/6}+\frac{6}{13}x^{13/6}-\frac{4}{15}x^{5/2}+\frac{1}{17}x^{17/6} \right \}+c$$
  • C. none of these
  • D. $$\displaystyle 6\left \{ x^{3/2}+\frac{4}{11}x^{11/6}+\frac{6}{13}x^{13/6}+\frac{4}{15}x^{5/2}+\frac{1}{17}x^{17/6} \right \}+c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q4 Subjective Medium
Evaluate the following $$\displaystyle \underset{1}{\overset{2}{\int}} \dfrac{5x^2}{x^2 + 4x + 3}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q5 Subjective Medium
$$\int { \cfrac { f'(x) }{ f(x) } dx } =\log { [f(x)] } +c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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