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
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### 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

Q2 Single Correct Hard
lf $f(x)$ is a polynomial of nth degree then $\displaystyle \int e^{x}f(x)dx=$
• A. $e^{x}[f(x)+f(x)+f^{'}(x)+f^{''}(x)+\ldots\ldots+(-1)^{n}J^{n}(x)]$
• B. $e^{x}[f(x)+f^{'}(x)+f^{'}(x)+f^{'''}(x)+\ldots\ldots+(-1)^{n}f^{2n}(x)]$
• C. $d[f(x)+f(x)+f^{'}(x)+f^{'''}(x)+\ldots\ldots+\{-1)^{n}f^{3n}(x)]$
• D. $e^{x}[f(x)-f^{'}(x)+f^{''}(x)-f^{'''}(x)+\ldots\ldots+(-1)^{n}f^{n}(x)]$ Where $f^{n}(x)$ denotes nth order derivative of w.r.t. $x$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

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

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

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

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