Download App

7.1 inderfinite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.1 inderfinite integral1 Mark
MCQ
$\int_{}^{} {\frac{{{e^x}dx}}{{\sqrt {a + b{e^x}} }}} = $
  • ✓
    $2/b\sqrt {a + b{e^x}} + c$
  • B
    $2b\sqrt {a + b{e^x}} + c$
  • C
    $\frac{1}{{2b}}\sqrt {a + b{e^x}} $
  • D
    $\frac{a}{b}\sqrt {a + b{e^x}} + c$
✓

Answer

Correct option: A.
$2/b\sqrt {a + b{e^x}} + c$
a
(a) Put $a + b{e^x} = t \Rightarrow b{e^x}dx = dt,$ then
$\int_{}^{} {\frac{{{e^x}dx}}{{\sqrt {a + b{e^x}} }}\, = \frac{1}{b}\int_{}^{} {\frac{1}{{\sqrt t }}\,dt = \frac{2}{b}\sqrt t + c} } $$ = \frac{{2\sqrt {a + b{e^x}} }}{b} + c.$

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 7.1 inderfinite integral→7.1 inderfinite integral — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Choose the correct answer from the given four option.
$\text{y}= \text{a}\text{e}^{\text{mx}}+\text{b}\text{e}^{-\text {mx}}$ satisfies which of the following differential equation?
  1. $\frac{\text{dy}}{\text{dx}}+\text {my}=0$
  2. $\frac{\text{dy}}{\text{dx}}-\text {my}=0$
  3. $\frac{\text{d}^2\text{y}}{\text{dx}^2}-\text{m} ^2\text{y}=0$
  4. $\frac{\text{d}^2\text{y}}{\text{dx}^2}+\text{m} ^2\text{y}=0$
→
Evaluate $ |\text{A}|^2-5|\text{A}|+1,$ if $\text{A}=\begin{bmatrix}7&4\\5&5\end{bmatrix}$ is:
  1. 161
  2. 251
  3. 150
  4. 151
→
If  $f(x) = \frac{{{e^{2x}} - {{(1 + 4x)}^{1/2}}}}{{\ln (1 - {x^2})}}$ for $x \ne 0,$ then $f$ has
→
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
→
Area of the region between the curves $\text{x}^2+\text{y}^2=\pi,\text{y}=\sin\text{x}$ and y-axis in first quadrant is:
  1. $\frac{\pi^3-8}{4\text{ sq.}\text{ units}}$
  2. $\frac{\pi^3-4}{4\text{ sq.}\text{ units}}$
  3. $\frac{\pi^3-8}{4\text{ sq.}\text{ units}}$
  4. $\frac{\pi^3-4}{4\text{ sq.}\text{ units}}$
→
Function $f(x)=2 x^3-15 x^2+36 x+6$ is increasing in which of interval :
→
Two persons $'A'$ and $'B'$ have respectively $n + 1$ and $n$ coins which they toss simultaneously. Then the probability that $A$ will have more heads than $B$ is
→
The distinct linear functions that map [-1, 1] onto [0, 2] are:
  1. f(x) = x + 1, g(x) = -x + 1
  2. f(x) = x - 1, g(x) = x + 1
  3. f(x) = -x - 1, g(x) = x - 1
  4. None of these.
→
A unit vector in the $xy - $ plane which is perpendicular to $4i - 3j + k$ 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
→