Download App

7.2 definite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.2 definite integral1 Mark
MCQ
If $f(x) = \left\{ {\begin{array}{*{20}{c}}{4x + 3\,,}&{{\rm{if}}}&{1 \le x \le 2}\\{3x + 5\,,}&{{\rm{if}}}&{2 < x \le 4}\end{array}} \right.$ then $\int_1^4 {\,f(x)} \,dx = $
  • A
    $80$
  • B
    $20$
  • C
    $ - 20$
  • ✓
    $37$
✓

Answer

Correct option: D.
$37$
d
(d) $\int_1^4 {f(x)dx = \int_1^2 {(4x + 3)dx + \int_2^4 {(3x + 5)\,dx} } } $

$ = \left| {2{x^2} + 3x} \right|_1^2 + \left| {\frac{{3{x^2}}}{2} + 5x} \right|_2^4 = 37$.

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 bounded by the curve $\text{y}=\log_{\text{e}}\text{x}$ and x-axis and the straight line x = e is:
  1. $\text{e sq. units}$
  2. $1\text{ sq. units}$
  3. $1-\frac{1}{\text{e}}\text{ sq. units}$
  4. $1+\frac{1}{\text{e}}\text{ sq. units}$
→
If the system of linear equations $x+ ay+z\,= 3$ ; $x + 2y+ 2z\, = 6$ ; $x+5y+ 3z\, = b$ has no solution, then
→
The solution of $y' - y = 1,\;y(0) = - 1$ is given by $y(x) = $
→
If $\omega $ is cube root of unity, then root of the equation $\left| {\begin{array}{*{20}{c}}
  {x + 2}&\omega &{{\omega ^2}} \\ 
  \omega &{x + 1 + {\omega ^2}}&1 \\ 
  {{\omega ^2}}&1&{x + 1 + \omega } 
\end{array}} \right| = 0$ is 
→
Let X1 and X2 are optimal solutions of a LPP, then:
  1. $\text{X}=\lambda\ \text{X}_1+(1-\lambda)\text{X}_2,\lambda\in$ R is also an optimal solution
  2. $\text{X}=\lambda\ \text{X}_1+(1-\lambda)\text{X}_2,0\leq\lambda\leq1$ given an optimal solution
  3. $\text{X}=\lambda\ \text{X}_1+(1+\lambda)\text{X}_2,0\leq\lambda\leq1$ given an optimal solution
  4. $\text{X}=\lambda\ \text{X}_1+(1+\lambda)\text{X}_2,\lambda\in$ R given an optimal solution
→
$\int_{}^{} {\frac{{dx}}{{(x - {x^2})}} = } $
→
Let $\vec{a}=\hat{i}-\hat{j}+2 \hat{k}$ and $\vec{b}$ be a vector such that $\vec{a} \times \vec{b}=2 \hat{i}-\hat{k}$ and $\vec{a} \cdot \vec{b}=3$. Then the projection of $\vec{b}$ on the vector $\vec{a}-\vec{b}$ is :-
→
The value of $k$ for which the function $f\left( x \right) = \left\{ \begin{gathered} {\left( {\frac{4}{5}} \right)^{\frac{{\tan \,4x}}{{\tan \,5x}}}},\,\,\,\,0 < x < \frac{\pi }{2} \hfill \\  k + \frac{2}{5}\,\,\,,\,\,\,\,\,\,\,\,\,\,\,x = \frac{\pi }{2} \hfill \\ \end{gathered}  \right.$ is continuous at  $x\,= \frac{\pi}{2}$ is
→
An unbiased coin is tossed $5$ times. Suppose that a variable $\mathrm{X}$ is assigned the value $\mathrm{k}$ when $\mathrm{k}$ consecutive heads are obtained for $\mathrm{k}=3,4,5$ otherwise $X$ takes the value $-1 .$ Then the expected value of $X,$ is
→
If $A =\left[\begin{array}{ll}1 & a \\ 0 & 1\end{array}\right]$ then $A ^4$ equals to :
→