_ -1 ^1 |x-2| x-2 d x, x 2 is equal to - Vidyadip

MCQ

$\int_{-1}^1 \frac{|x-2|}{x-2} d x, x \neq 2$ is equal to

A
1
B
-1
C
2
D
-2

✓

Answer

Let $I=\int_{-1}^1 \frac{|x-2|}{x-2} d x$
$
=\int_{-1}^1 \frac{-(x-2)}{x-2} d x=\int_{-1}^1-1 \cdot d x=[-x]_{-1}^1=-[1-(-1)]=-2
$

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

Let $f$ and $g$ be increasing and decreasing functions, respectively from $[0 , \infty )$ to $[0 , \infty )$. Let $h (x) = f [g (x)]$ . If $h (0) = 0$, then $ h (x) - h (1)$ is

Choose the correct answer from the given four options. Two dice are thrown. If it is known that the sum of numbers on the dice was less than $6,$ the probability of getting a sum $3,$ is:

If $A = \{1, 2, 3\}; B = \{3, 4, 5\}; C = \{4, 6\},$ then $\text{A}\times(\text{B}\cap\text{C})=?$

A function f from the set of natural numbers to integers defined by $\text{f(n)}=\begin{cases}\frac{\text{n}-1}{2},&\text{when n is odd}\\-\frac{\text{n}}{2},&\text{when n is even}\end{cases}$

Let $f(x) = sin\ x, g(x) = cos\ x$ , then which of the following statement is false

The solution of $\frac{\text{dy}}{\text{dx}}=1+\text{x}+\text{y}+\text{xy}$ is:

The position vectors of $ P$ and $ Q $ are $5i + 4j + ak$ and $ - i + 2j - 2k$ respectively. If the distance between them is $7,$ then the value of $a$ will be

If $S$ is the sum of the first $10$ terms of the series $\tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\left(\frac{1}{7}\right)+\tan ^{-1}\left(\frac{1}{13}\right)+\tan ^{-1}\left(\frac{1}{21}\right)+\ldots$ then $\tan ( S )$ is equal to

The maximum value of Z = 3x + 4y subjected to constraints $\text{x}+\text{y}\leq4,\text{x}\geq0$ and $\text{y}\geq0$ is:

Choose the correct option from given four options$:\ \int\frac{\text{x}+\sin\text{x}}{1+\cos\text{x}}\text{dx}$ is equal to: