Download App

7.2 definite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.2 definite integral1 Mark
MCQ
$\int_0^{\pi /2} {{{\sin }^2}x{{\cos }^3}x} \,dx = $
  • A
    $0$
  • ✓
    $\frac{2}{{15}}$
  • C
    $\frac{4}{{15}}$
  • D
    None of these
✓

Answer

Correct option: B.
$\frac{2}{{15}}$
b
(b) Using gamma function,

$\int_0^{\pi /2} {{{\sin }^2}x{{\cos }^3}xdx = \frac{{\Gamma \,\left( {\frac{3}{2}} \right)\,\Gamma 2}}{{2\Gamma \left( {\frac{7}{2}} \right)}} = \frac{2}{{15}}} $.

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

More "M.C.Q (1 Marks)" from 7.2 definite integral→7.2 definite integral — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The area of the triangle formed by the tangent to the hyperbola $xy = {a^2}$ and co-ordinate axes is
→
If the function $f\left( x \right) = \left\{ \begin{array}{l}
a\,\left| {\pi  - x} \right|\, + 1,\,\,x \le 5\,\\
b\,\,\left| {\pi  - x} \right|\, + 3,\,\,x > 5\,\,
\end{array} \right.$ is continuous at $x = 5$, then the value of $a -b$ is
→
If $\sin ^{-1} \frac{\alpha}{17}+\cos ^{-1} \frac{4}{5}-\tan ^{-1} \frac{77}{36}=0,0 < \alpha < 13$, then $\sin ^{-1}(\sin \alpha)+\cos ^{-1}(\cos \alpha)$ is equal to $.........$.
→
Let $S=\{1,2,3,4,5,6\}$. Then the number of oneone functions $f: S \rightarrow P(S)$, where $P(S)$ denote the power set of $S$, such that $f(n) \subset f(m)$ where $n < m$ is $..................$
→
A particle moves in a straight line with a velocity given by $\frac{{dx}}{{dt}} = x + 1$($x$ is the distance described). The time taken by a particle to traverse a distance of $99$ metre is
→
For all values of $A,B,C$ and $P,Q,R$, the value of $\left| {\,\begin{array}{*{20}{c}}{\cos (A - P)}&{\cos (A - Q)}&{\cos (A - R)}\\{\cos (B - P)}&{\cos (B - Q)}&{\cos (B - R)}\\{\cos (C - P)}&{\cos (C - Q)}&{\cos (C - R)}\end{array}\,} \right|$ is
→
Let $\vec a\, = \,\hat i\, + \,\hat j\, + \,\sqrt 2 \hat k,\,\,\vec b\, = \,{b_1}\hat i\, + \,{b_2}\hat j\, + \sqrt 2 \hat k$ and $\vec c\, = \,5\hat i\, + \,\hat j + \sqrt 2 \hat k$ be three vectors such that the projection vector of $\vec b$ on $\vec a$ is $\vec a$. If $\vec a\, + \vec b$ is perpendicular to $\vec c$ , then $\left| {\vec b} \right|$ is equal to
→
$\int {\frac{{\cos 2x - 1\,\,}}{{\cos 2x + 1}}dx = } $
→
In a college 30% students fail in Physics, 25% fail in Mathenatics and 10% fail in both. One student is chosen at random. The probability that she fails in Physics if she failed in Mathematics is.
→
If $(\cos x)^y=(\cos y)^x$, then $\frac{d y}{d x}$ is equal to:
→