Download App

Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals1 Mark
MCQ
Evaluate : $\int_0^2 e^{3-4 x} d x$
  • A
    $\frac{-1}{4}\left(e^5-e^3\right)$
  • B
    $\frac{1}{4}\left(e^5-e^3\right)$
  • C
    $\frac{1}{4}\left(e^{-5}-e^3\right)$
  • ✓
    $\frac{-1}{4}\left(e^{-5}-e^3\right)$
✓

Answer

Correct option: D.
$\frac{-1}{4}\left(e^{-5}-e^3\right)$
We have$, \int_0^2 e^{3-4 x} d x=\left[\frac{e^{3-4 x}}{-4}\right]_0^2$
$=-\frac{1}{4}\left[e^{3-8}-e^{3-0}\right]=\frac{-1}{4}\left[e^{-5}-e^3\right]$

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 Integrals→Integrals — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Let$\begin{vmatrix}\text{x}&2&\text{x}\\\text{x}^2&\text{x}&6\\\text{x}&\text{x}&6\end{vmatrix}=\text{ax}^4+\text{bx}^3+\text{cx}^2+\text{dx}+\text{e}.$ Then, the value of $5a + 4b + 3c + 2d + e$ is equal to:
→
$\text{Let A}=\begin{bmatrix}1&\sin\theta&1\\-\sin\theta&1&\sin\theta\\-1&-\sin\theta&1\end{bmatrix},$ where $0\leq\theta\leq2\pi.$ Then
→
The set of all values of $ ' a '$ for which the function , $f (x) = (a^2 - 3 a + 2) \left( {{{\cos }^{2\,}}\,\frac{x}{4}\,\, - \,\,{{\sin }^2}\,\,\frac{x}{4}} \right) + (a - 1) x + sin \,1 $ does not possess critical points is
→
Consider function $f: A \rightarrow B$ and $g: B \rightarrow C(A, B, C \subseteq R)$ such that $(gof) ^{-1}$ exists, then:
→
$\cos^{-1}\frac{\text{x}}{\text{a}}+\cos^{-1}\frac{\text{y}}{\text{b}}=\alpha,$ then $\frac{\text{x}^2}{\text{a}^2}-\frac{2\text{xy}}{\text{ab}}\cos\alpha+\frac{\text{y}^2}{\text{b}^2}=$
→
Consider $f(x) = \left\{ \begin{array}{l}\frac{{{x^2}}}{{|x|}},\,x \ne 0\\\,\,\,\,\,\,\,0,\,x = 0\end{array} \right.$
→
If $A=\left[\begin{array}{rr}2 & -1 \\ 1 & 3\end{array}\right]$, then $A ^{-1}= ?$
→
Let $a, b, c \in R$ be all non-zero and satisfy $a^{3}+b^{3}+c^{3}=2 .$ If the matrix $A=\left(\begin{array}{lll}a & b & c \\ b & c & a \\ c & a & b\end{array}\right)$ satisfies $\mathrm{A}^{\mathrm{T}} \mathrm{A}=\mathrm{I},$ then a value of $abc$ can be
→
Choose the correct answer from given four options in each of the Exercise : If $A, B$ and $C$ are angles of a triangle, then the determinant $\begin{vmatrix}-1&\cos\text{C}&\cos\text{B}\\\cos\text{C}&-1&\cos\text{A}\\\cos\text{B}&\cos\text{A}&-1\end{vmatrix}$ is equal to :
→
Let $f(\mathrm{x})=\mathrm{x} \cos ^{-1}(-\sin |\mathrm{x}|), \quad \mathrm{x} \in\left[-\frac{\pi}{2}, \frac{\pi}{2}\right],$ then which of the following is true?
→