Mathematics

Evaluate: $$\displaystyle \int_{0}^{\pi/2} \sin^2 x. \cos^3 x \ dx.$$


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Subjective Medium Published on 17th 09, 2020
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Realted Questions

Q1 Single Correct Medium
If $$f(x)$$ is an odd function, then $$\int_{-a}^a f(x) dx$$ is
  • A. $$2 \int_0^a f(x) dx$$
  • B. $$\int_0^a f(x) dx$$
  • C. $$\int_0^a f(a - x) dx$$
  • D. $$0$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q2 Single Correct Hard
lf $$f(x)$$ is a polynomial of nth degree then $$\displaystyle \int e^{x}f(x)dx=$$
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  • B. $$e^{x}[f(x)+f^{'}(x)+f^{'}(x)+f^{'''}(x)+\ldots\ldots+(-1)^{n}f^{2n}(x)]$$
  • C. $$d[f(x)+f(x)+f^{'}(x)+f^{'''}(x)+\ldots\ldots+\{-1)^{n}f^{3n}(x)]$$
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Asked in: Mathematics - Integrals


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Q3 Subjective Medium
Solve : $$\overset{\frac{\pi}{2}}{\displaystyle\int_0} x^2 \sin \, x \, dx$$

Asked in: Mathematics - Integrals


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Q4 Single Correct Hard
$$\int_{0}^{\pi/2}\dfrac{\phi (x)}{\phi(x)+\phi(\pi/2-x)}dx=$$

  • A. $$\pi/2$$
  • B. $$\pi$$
  • C. $$\pi/3$$
  • D. $$\pi/4$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q5 Passage Medium
The average value of a function f(x) over the interval, [a,b] is the number $$\displaystyle \mu =\frac{1}{b-a}\int_{a}^{b}f\left ( x \right )dx$$
The square root $$\displaystyle \left \{ \frac{1}{b-a}\int_{a}^{b}\left [ f\left ( x \right ) \right ]^{2}dx \right \}^{1/2}$$ is called the root mean square of f on [a, b]. The average value of $$\displaystyle \mu $$ is attained id f is continuous on [a, b].

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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