Download App

7.2 definite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.2 definite integral1 Mark
MCQ
$\int\limits_0^{\sqrt 3 } {{{\left( {x + 4} \right)}^2}{e^{{x^2}}}dx + \int\limits_{\sqrt 3 }^0 {{{\left( {x - 4} \right)}^2}{e^{{x^2}}}dx} } $ is equal to
  • A
    $8e^3$
  • ✓
    $8(e^3 -1)$
  • C
    $\sqrt 3 \left( {{e^4} - 1} \right)$
  • D
    $\sqrt 3 \left( {{e^8} - 1} \right)$
✓

Answer

Correct option: B.
$8(e^3 -1)$
b
$\int_{0}^{\sqrt{3}} e^{x^{2}}\left\{(x+4)^{2}-(x-4)^{2}\right\} d x$

$\left.=\int_{0}^{\sqrt{3}} \mathrm{e}^{\mathrm{x}^{2}} 16 \mathrm{x} \mathrm{\,dx}=8 \mathrm{e}^{\mathrm{x}^{2}}\right)_{0}^{\sqrt{3}}=8\left(\mathrm{e}^{3}-1\right)$

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

$M$ and $N$ are two events such that $P(M \cap N)=0$. Which of the following is equal to $P(M \mid(M \cup N))$ ?
→
A function $y = f (x)$ satisfying the differential equation $\frac{{dy}}{{dx}} \cdot \sin x - y \cos x + \frac{{{{\sin }^2}x}}{{{x^2}}} = 0$ is such that, $y \rightarrow  0$ as $x \rightarrow \infty$ then the statement which is correct is
→
If $f(x)\, = \,\,\left\{ {\begin{array}{*{20}{c}}{\frac{{x - 1}}{{2{x^2} - 7x + 5}}}&{{\rm{for \,\,}}x \ne 1}\\{ - \frac{1}{3}}&{{\rm{for\,\, }}x = 1}\end{array}\,\,,} \right.$ then $f'(1) = $
→
Spherical rain drop evaporates at a rate proportional to its surface area. The differential equation corresponding to the rate of change of the radius of the rain drop if the constant of proportionality is $K > 0,$ is
→
If $\tan^{-1}\Big(\frac{\text{x}-1}{\text{x}+2}\Big)+\tan^{-1}\Big(\frac{\text{x}+1}{\text{x}+2}\Big)=\frac{\pi}{4},$ then x is equal to:
  1. $\frac{1}{\sqrt{2}}$
  2. $-\frac{1}{\sqrt2}$
  3. $\pm\sqrt{\frac{5}{2}}$
  4. $\pm\frac{1}{2}$
→
Given a system of inequation: $2\text{y}-\text{x}\leq4$ $-2\text{x}+\text{y}\geq-4$Find the value of s, which is the greatest possible sum of the x and y co - ordinates of the point which satisfies the following inequalities as graphed in the xy plane.
  1. 8
  2. 12
  3. 2
  4. 4
→

A five-digit number is written down at raddom. The probability that the number is divisible by 5, and no two consecutive digits are identical, is:

→
Let a function $f: R \rightarrow R$ be defined as

$f(x)=\sin x-e^{x} \,\,\,\, \text { if } x \leq 0$

$\quad\quad\quad a+[-x] \,\,\,\, \text { if } 0\,<\,x\,<\,1$

$\quad\quad\quad 2 x-b \,\,\,\,\,\,\,\, \text { if } \geq 1$

where $[\mathrm{x}]$ is the greatest integer less than or equal to $\mathrm{x}$. If $\mathrm{f}$ is continuous on $\mathrm{R}$, then $(\mathrm{a}+\mathrm{b})$ is equal to:

→
The differential equation of all parabolas each of which has a latus rectum $'4a'$ $\&$ whose axes are parallel to $x-$ axis is :
→
$\int_{}^{} {\frac{x}{{\sqrt {4 - {x^4}} }}dx} = $
→