Download App

STD 12 - 7.2 definite integral — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 7.2 definite integral1 Mark
MCQ
$\int_{ - \pi /4}^{\pi /2} {{e^{ - x}}\sin x\,dx} = $
  • ✓
    $ - \frac{1}{2}{e^{ - \pi /2}}$
  • B
    $ - \frac{{\sqrt 2 }}{2}{e^{ - \pi /4}}$
  • C
    $ - \sqrt 2 ({e^{ - \pi /4}} + {e^{ - \pi /4}})$
  • D
    $0$
✓

Answer

Correct option: A.
$ - \frac{1}{2}{e^{ - \pi /2}}$
a
(a) $\int_{ - \pi /4}^{\pi /2} {{e^{ - x}}\sin x\,dx} $

$= \left[ {\frac{{{e^{ - x}}}}{2}( - \sin x - \cos x)} \right]_{ - \pi /4}^{\pi /2}$

$ = \frac{1}{2}[{e^{ - x}}( - \sin x - \cos x)]_{ - \pi /4}^{\pi /2}$

$ = \frac{1}{2}\left[ {{e^{ - \pi /2}}( - 1 - 0) - \left\{ {{e^{\pi /4}}\left( {\frac{1}{{\sqrt 2 }} - \frac{1}{{\sqrt 2 }}} \right)} \right\}} \right] $

$= - \frac{{{e^{ - \pi /2}}}}{2}$.

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 STD 12 - 7.2 definite integral→STD 12 - 7.2 definite integral — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

Let a vector $\vec{a}$ be coplanar with vectors $\vec{b}=2 \hat{i}+\hat{j}+\hat{k}$ and $\vec{c}=\hat{i}-\hat{j}+\hat{k} .$ If $\vec{a}$ is perpendicular to $\vec{d}=3 \vec{i}+2 \hat{j}+6 \hat{k}$, and $|\vec{a}|=\sqrt{10} .$ Then a possible value of $[\overrightarrow{\mathrm{a}} \overrightarrow{\mathrm{b}} \overrightarrow{\mathrm{c}}]+[\overrightarrow{\mathrm{a}} \overrightarrow{\mathrm{b}} \vec{d}]+[\overrightarrow{\mathrm{a}} \vec{c} \vec{d}]$ is equal to:
→
Evaluate: $\int\sec^{\frac{4}{3}}\text{x}\text{cosec}^{\frac{8}{3}}\text{xdx}.$
→
If a plane passes through the point (1, 1, 1) and is perpendicular to the line $\frac{\text{x}-1}{3}=\frac{\text{y}-1}{0}=\frac{\text{z}-1}{4}$ then its perpendicular distance from the origin is:
→
Tho damnin of tho finction $\cos ^{-1}\left(\frac{2 \sin ^{-1}\left(\frac{1}{4 x^{2}-1}\right)}{\pi}\right)$ is
→
If $\text{f(x)}=\begin{cases}\frac{36^\text{x}-9^\text{x}-4\text{x}+1}{\sqrt{2}-\sqrt{1+\cos\text{x}}},&\text{x}\neq0\\\text{k},&\text{x}=0\end{cases}$ is continuous at $x = 0$, these $k$ equals.
→
$\int\frac{\sin\text{x} + \cos\text{x}}{\sqrt{(1 + \sin2\text{x})}}\text{dx}$ is :
→
If $l\,a + m\,b + n\,c = 0,$ where $l,\,m,\,\,n$ are scalars and $a, b, c $ are mutually perpendicular vectors, then
→
If $f (x) = \int\limits_0^\pi  {\frac{{t\,\sin t\,dt}}{{\sqrt {1 + {{\tan }^2}x\,\,\,{{\sin }^2}t} }}\,} $  for $0 < x < \frac{\pi }{2}\,$
→
The function ${{x - 2} \over {x + 1}},(x \ne - 1)$ is increasing on the interval
→
Volume of the parallelopiped whose coterminous edges are $2i - 3j + 4k,\,\,i + 2j - 2k,\,\,3i - j + k,$ is ............ $\mathrm{cubic\,unit}$
→