Evaluate the following integrals: ^2_02x [x ]dx - Vidyadip

Question

Evaluate the following integrals:
$\int\limits^2_02\text{x}\big[\text{x}\big]\text{dx}$

✓

Answer

[x] = 0 for 0
and [x] = 1 for 1
Hence,
$=\int\limits^1_10+\int\limits^2_12\text{x}\text{ dx}$
$=\big\{\text{x}^2\big\}^2_1$
$=3$

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 "2 Marks Questions" from Definite Integrals→Definite Integrals — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

If $\begin{bmatrix}\text{x}&2\end{bmatrix}\begin{bmatrix}3\\4\end{bmatrix}=2,$ find x.

If $\text{f(x)}=\log_\text{e}(\log_\text{e}\text{x}),$ then write the value of f'(e).

Evaluate the following integrals:
$\int\frac{1}{\text{x}^5}\text{dx}$

Evalute the following integrals:
$\int\frac{\sec\text{x}\tan\text{x}}{3\sec\text{x}+5}\text{dx}$

A discrete random variable $X$ has the probability distribution given below:

$X:$	$0.5$	$1$	$1.5$	$2$
$P(X):$	$k$	$k^2$	$2k^2$	$k$

Find the value of $k.$

Find $\frac{\text{dy}}{\text{dx}}$ when x and y are connected by the relation:
$\tan^{-1}(\text{x}^2+\text{y}^2)=\text{a}$

6 boys and 6 girls sit in a row at random. Find the probability that all the girls sit together.

If $\vec{\text{a}}=\hat{\text{i}}-\hat{\text{j}}$ and $\vec{\text{b}}=-\hat{\text{j}}+\hat{\text{k}},$ find the projection of $\vec{\text{a}}$ on $\vec{\text{b}}.$

Prove that the logarithmic function is increasing on $(0, \infty)$.

Let * be a binary operation on the set I of integers, defined by a * b = 2a + b - 3. Find the value of 3 * 4.