Mathematics

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

Q1 Single Correct Medium
Evaluate $$\displaystyle\int^{\pi/2}_0\sin^2xdx$$
  • A. $$\dfrac{\pi}{3}$$
  • B. $$\dfrac{\pi}{2}$$
  • C. $$\dfrac{2\pi}{3}$$
  • D. $$\dfrac{\pi}{4}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q2 Single Correct Hard
Evalaute the integral
$$\displaystyle \int_{0}^{\pi}xf(\sin x)dx$$
  • A. $$ 2\pi$$
  • B. $$\displaystyle \pi\int_{0}^{\pi}f(\cos x)dx$$
  • C. $$\displaystyle \pi\int_{0}^{\pi}f(\sin x) dx$$
  • D. $$\displaystyle \pi\int_{0}^{\pi/2}f(\cos x)dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q3 Single Correct Medium
The integral of $$f(x) = \dfrac{1}{x\ell n x} $$ is
  • A. $$x \ell n x + c$$
  • B. $$\dfrac{x}{\ell n x} + c$$
  • C. $$x + \ell n x + $$
  • D. $$\ell n(\ell n x) + c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q4 Subjective Medium
Integrate the function    $$x \sin 3x$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q5 Single Correct Medium

$$\displaystyle \int_{0}^{a}\frac{x^{5}dx}{\sqrt{a^{2}-x^{2}}}=$$
  • A. $$\displaystyle \frac{\mathrm{a}^{5}}{15}$$
  • B. $$\displaystyle \frac{8a}{15}$$
  • C. $$\displaystyle \frac{11\mathrm{a}^{2}}{15}$$
  • D. $$\displaystyle \frac{8\mathrm{a}^{5}}{15}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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