_0^ /2 ^4 x ^6 x ,dx equals - Vidyadip

MCQ

$\int_0^{\pi /2} {{{\sin }^4}x{{\cos }^6}x\,dx} $ equals

A
$\frac{{5\pi }}{{512}}$
✓
$\frac{{3\pi }}{{512}}$
C
$\frac{\pi }{{512}}$
D
None of these

✓

Answer

Correct option: B.

$\frac{{3\pi }}{{512}}$

b
(b) $I = \int_0^{\pi /2} {{{\sin }^4}x{{\cos }^6}x.dx} $

$ \Rightarrow I = \frac{{\Gamma \,(5/2)\,\Gamma \,(7/2)}}{{2\Gamma (6)}}$, (Applying gamma function)

==> $I = \frac{{3/2.1/2.\sqrt \pi .5/2.3/2.1/2.\sqrt \pi }}{{2.5.4.3.2.1}}$

$ = \frac{{3\pi }}{{512}}$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Let $P \left(\frac{2 \sqrt{3}}{\sqrt{7}}, \frac{6}{\sqrt{7}}\right), Q , R$ and $S$ be four points on the ellipse $9 x^2+4 y^2=36$. Let $P Q$ and $RS$ be mutually perpendicular and pass through the origin. If $\frac{1}{( PQ )^2}+\frac{1}{( RS )^2}=\frac{ p }{ q }$, where $p$ and $q$ are coprime, then $p+q$ is equal to $.........$.

Let $\lambda \in R$ and let the equation $E$ be $| x |^2-2| x |+|\lambda-3|=0$. Then the largest element in the set $S =$ $\{ x +\lambda: x$ is an integer solution of $E \}$ is $..........$

If $ ABCDEF$ is a regular hexagon and $\overrightarrow {AB} + \overrightarrow {AC} + \overrightarrow {AD} + \overrightarrow {AE} + \overrightarrow {AF} = \lambda \,\overrightarrow {AD} ,$ then $\lambda = $

The sum of all rational terms in the expansion of $(2+\sqrt{3})^8$ is

The domain of the function $f(x) = {\log _{3 + x}}({x^2} - 1)$ is

If $\frac{{\sec \,8\theta - 1}}{{\sec \,4\theta - 1}} = \frac{{a + b\,{{\tan }^2}2\theta }}{{1 + c\,{{\tan }^2}\,2\theta + d\,{{\tan }^4}2\theta }}$

(where $\theta \ne \frac{{n\pi }}{{16}},n \in I$ ), then value of $(a -b + c -d)$ is -

If the standard deviation of $0, 1, 2, 3, …..,9$ is $K$, then the standard deviation of $10, 11, 12, 13 …..19$ is

The point having position vectors $2i + 3j + 4k,\,\,$ $3i + 4j + 2k,$ $4i + 2j + 3k$ are the vertices of

$\mathop {\lim }\limits_{x \to 0} \,x^2(1+2+3+...+[\frac{1}{|x|}])$ is equal to

(where [.] denotes greatest integer function)

The number of ways in which $5$ boys and $3$ girls can be seated on a round table if a particular boy $B_1$ and a particular girl $G_1$ never sit adjacent to each other, is