The value of x d x : - Vidyadip

Question

The value of $\int \log x d x$ :

✓

Answer

(C)
$\int_{\text {II }}^1 1 \cdot \log x \cdot d x=\log x \cdot x-\int \frac{1}{x} \times x d x$
$=x \log x-x=x(\log x-1)+c$

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→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

The distance of the line $\vec{\text{r}}=2\hat{\text{i}}-2\hat{\text{j}}+3\hat{\text{k}}+\lambda(\hat{\text{i}}-\hat{\text{j}}+4\hat{\text{k}})$ from the plane $\vec{\text{r}}.(\hat{\text{i}}+5\hat{\text{j}}+\hat{\text{k}})=5$ is:

Area of the region bounded by the curve $\text{y}=\cos\text{x}$ between x = 0 and $\text{x}=\pi$ is:

2 sq. units
4 sq. units
3 sq. units
1 sq. units

If $P(A)=\frac{3}{5}, P(B)=\frac{1}{5}$ and $A$, $B$ are independent events then $P(A \cap B)$ is -

If a line makes angles of $90^{\circ}, 135^{\circ}, 45^{\circ}$ with $x, y$ and $z$ axes, then its direction cosines will be :

The differential equation obtained on eliminating A and B from $\text{y}=\text{A}\cos\omega\text{t}+\text{B}\sin\omega\text{t}$ is:

$\text{y}''+\text{y}'=0$
$\text{y}''-\omega^{2}\text{y}=0$
$\text{y}''=-\omega^{2}\text{y}=0$
$\text{y}''+\text{y}=0$

If $A$ is a square matrix such that $A^2 = I,$ then $(A - I)^3 + (A + I)^3 - 7A$ is equal to:

Let $f: R \rightarrow R$ be defined as $f(x)=x^3$. Choose the correct answer.

What is the value of $\int_{-1}^{1}\sin^3\text{x}\cos^2\text{xdx}?$

$0$
$1$
$\frac{1}{2}$
$2$

Direction ratio of line joining (2, 3, 4) and (-1, -2, 1), are:

(-3, -5, -3)
(-3, 1, -3)
(-1, -5, -3)
(-3, -5, 5)

A bag contains 5 red and 3 blue balls. If 3 balls are drawn at random without replacement, then the probability that exactly two of the three balls were red, the first ball being red, is