(1+2x+3x^2+4x^3+ ... )dx ( <1) - Vidyadip

MCQ

$\int(1+2\text{x}+3\text{x}^2+4\text{x}^3+ ... )\text{dx }(\mid\text{x}\mid<1)$

A
$-(1+\text{x})^{-1}+\text{c}$
✓
$(1-\text{x})^{-1}+\text{c}$
C
$-(1-\text{x})^{-2}+\text{c}$
D
None of these

✓

Answer

Correct option: B.

$(1-\text{x})^{-1}+\text{c}$

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 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

In a tournament, a team plays $10$ matches with probabilities of winning and losing each match as $\frac{1}{3}$ and $\frac{2}{3}$ respectively. Let $x$ be the number of matches that the team wins, and $y$ be the number of matches that team loses. If the probability $\mathrm{P}(|\mathrm{x}-\mathrm{y}| \leq 2)$ is $\mathrm{p}$, then $3^9 \mathrm{p}$ equals....................

The distance of the point having position vector $ - \,\hat i\, + \,2\hat j\, + 6\hat k$ from the straight line passing through the point $(2, 3, -4)$ and parallel to the vector $6\,\hat i\, + 3\hat j\, - 4\hat k$ is

If a line makes angles $\frac{\pi}{4}, \frac{3 \pi}{4}$ with $X-$axis and $Y-$axis respectively, then the angle which it makes with $Z-$axis is

If $\frac{\text{d}}{\text{dx}}[\text{x}^\text{n}-\text{a}_1\text{x}^{\text{n}-1}+\text{a}_2\text{x}^{\text{n}-2}+...+(-1)^\text{n}\text{a}_\text{n }]\text{e}^\text{x}=\text{x}^\text{n}\ \text{e}^\text{x},$ then the value of a, 0 < r < is equals to:

Let the vectors $\vec{a}\ \text{and}\ \vec{b}$ be such that $|\vec{a}|=3\ \text{and}\ \big|\vec{b}\big|=\frac{\sqrt{2}}{3},\ \text{then}\ \vec{a}\times\vec{b}$ is a unit vector, if the angle between $\vec{a}\ \text{and}\ \vec{b}\ \text{is}$

$\int_{}^{} {\frac{{dx}}{{1 + x + {x^2} + {x^3}}} = } $

$\int_{}^{} {\frac{{\sin x\;dx}}{{{{(a + b\cos x)}^2}}} = } $

If the function $\text{f(x)}=\frac{2\text{x}-\sin^{-1}\text{x}}{2\text{x}+\tan^{-1}\text{x}}$ is continuous at each point of its domain, then the value of f(0) is:

If $y = {x^{\sqrt x }},$then ${{dy} \over {dx}} =$

Suppose the vectors $x_{1}, x_{2}$ and $x_{3}$ are the solutions of the system of linear equations, $Ax = b$ when the vector $b$ on the right side is equal to $b _{1}, b _{2}$ and $b _{3}$ respectively. If $x =\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right], x _{2}=\left[\begin{array}{l}0 \\ 2 \\ 1\end{array}\right], x _{3}=\left[\begin{array}{l}0 \\ 0 \\ 1\end{array}\right], b _{1}=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]$ $b _{2}=\left[\begin{array}{l}0 \\ 2 \\ 0\end{array}\right]$ and $b _{3}=\left[\begin{array}{l}0 \\ 0 \\ 2\end{array}\right],$ then the determinant of $A$ is equal to