Download App

7.2 definite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.2 definite integral1 Mark
MCQ
Let $\mathrm{a}$ and $\mathrm{b}$ be real constants such that the function $f$ defined by $f(x)=\left\{\begin{array}{cc}x^2+3 x+a & x \leq 1 \\ b x+2, & x>1\end{array}\right.$ be differentiable on $R$. Then, the value of $\int_{-2}^2 f(x) d x$ equals
  • A
     $\frac{15}{6}$
  • B
    $\frac{19}{6}$
  • C
     $21$
  • ✓
    $17$
✓

Answer

Correct option: D.
$17$
d
$ \mathrm{f} \text { is continuous } \quad \mathrm{f}^{\prime}(\mathrm{x})=2 \mathrm{x}+3, \mathrm{x}<1 $

$ \therefore 4+\mathrm{a}=\mathrm{b}+2$

$ \text { b }, x>1 $

$ \mathrm{a}=\mathrm{b}-2 \quad \mathrm{f} \text { is differentiable } $

$ \therefore \mathrm{b}=5 $

$ \therefore \quad \mathrm{a}=3 $

$ \int_{-2}^1\left(x^2+3 x+3\right) d x+\int_1^2(5 x+2) d x $

$ =\left[\frac{\mathrm{x}^3}{3}+\frac{3 \mathrm{x}^2}{2}+3 \mathrm{x}\right]_{-2}^1+\left[\frac{5 \mathrm{x}^2}{2}+2 \mathrm{x}\right]_1^2$

$ =\left(\frac{1}{3}+\frac{3}{2}+3\right)-\left(\frac{-8}{3}+6-6\right)+\left(10+4-\frac{5}{2}-2\right)$

$ =6+\frac{3}{2}+12-\frac{5}{2}=17 $

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

If $\text{A}=\begin{bmatrix}1&-1\\2&-1\end{bmatrix},\text{B}=\begin{bmatrix}\text{a}&1\\\text{b}&-1\end {bmatrix}$ and (A + B)2 = A2 + B2, values of a and b are:
  1. a = 4, b = 1
  2. a = 1, b = 4
  3. a = 0, b = 4
  4. a = 2, b = 4
→
Let $A=\left(\begin{array}{cc}4 & -2 \\ \alpha & \beta\end{array}\right)$ . If $A ^{2}+\gamma A +18 I = O$, then $\operatorname{det}( A )$ is equal to
→
Time period is a:
  1. Vector quantity
  2. Scalar quantity
  3. Neither scalar nor vector
  4. None of these
→
If ABCDEF is a regular hexagon, then $\overrightarrow{\text{AD}}+\overrightarrow{\text{EB}}+\overrightarrow{\text{FC}}$ equals,
  1. $2\overrightarrow{\text{AB}}$
  2. $\vec0$
  3. $3\overrightarrow{\text{AB}}$
  4. $4\overrightarrow{\text{AB}}$
→
The value of ${\sin ^{ - 1}}(\sin \,100) + \,{\cos ^{ - 1}}(\cos \,100) + {\tan ^{ - 1}}\,(\tan \,100) + {\cot ^{ - 1}}(\cot \,100)$
→
Evaluate: $\int[\sin (\log x)+\cos (\log x)] d x$
→
If $y = \sqrt {{{1 + x} \over {1 - x}}} ,$ then ${{dy} \over {dx}} = $
→
The value of $I = \int_0^{\pi /2} {\frac{{{{(\sin x + \cos x)}^2}}}{{\sqrt {1 + \sin 2x} }}{\rm{ }}} dx$ is
→
The probabilities of a student getting I, II and III division in an examination are $\frac{1}{10},\frac{3}{5}$ and $\frac{1}{4}$ respectively. The probability that the student fails in the examination is.
  1. $\frac{197}{200}$
  2. $\frac{27}{100}$
  3. $\frac{83}{100}$
  4. None of these.
→
$a=i+j+k,\,b=2i-4k,\,c=i+\lambda \,j+3k$  are coplanar, then the value of $\lambda $ is
→