Evaluate the definite integral _ -1 ^ 1 (x+1) d x - Vidyadip

Question

Evaluate the definite integral $\int_{-1}^{1}(x+1) d x$

✓

Answer

Let $I=\int_{-1}^{1}(x+1) d x$
$I=\int_{-1}^{1}(x+1) d x$
$\Rightarrow \mathrm{I}=\int_{-1}^{1} \mathrm{x} \mathrm{dx}+\int_{-1}^{1} 1 \cdot \mathrm{dx} ~~~~~\left[As \int \mathrm{x}^{\mathrm{n}} \mathrm{d} \mathrm{x}=\frac{\mathrm{x}^{\mathrm{n}+1}}{\mathrm{n}+1}\right]$
$\Rightarrow I=\left[\frac{x^{2}}{2}\right]_{-1}^{1}+[x]_{-1}^{1}$
$\Rightarrow \mathrm{I}=\left[\frac{1^{2}}{2}-\frac{(-1)^{2}}{2}\right]+[1-(-1)]$
$\Rightarrow I=\left[\frac{1}{2}-\frac{1}{2}\right]+[1+1]=0+2$
$\Rightarrow$ I = 2
$\int_{-1}^{1}(x+1) d x=2$

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 "2 Marks Questions" 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

A random variable has the following probability distribution:

$X = X_i$	$1$	$2$	$3$	$4$
$P(X = X_i)$	$k$	$2k$	$3k$	$4k$

Write the value of $\text{P}(\text{X}\geq3).$

Find $\frac{d y}{d x}$ if $y = \sin^{–1}\left(\frac{2 x}{1+x^{2}}\right)$

If a line makes angles 90º, 135º, 45º with the x, y and z-axes respectively, find its direction cosines.

If $x=t^2, y=t^3$ then find $\frac{d^2 y}{d x^2}$.

Find the vector equation one of following plane.
x + y = 3

Let $R_0$ denote the set of all non-zero real numbers and let $A = R_0 \times R_0.$ If $'*'$ is a binary operation on adefined by,
$(a, b) * (c, d) = (ac, bd)$ for all $(a, b), (c, d) \in A$
Find the invertible element in $A$.

If $\text{A}=\begin{bmatrix}2 & 0 & 1 \\2 & 1 & 3\\1 & -1 & 0 \end{bmatrix},$ then find $(\text{A}^2-5\text{A}).$

Write the value of $\cos^{-1}(\cos6).$

For any two vectors $\vec{\text{a}}$ and $\vec{\text{b}},$ find $\big(\vec{\text{a}}\times\vec{\text{b}}\big).\vec{\text{b}}.$

Evaluate the following determinant:
$\begin{vmatrix}1&4&9\\4&9&16\\9&16&25 \end{vmatrix}$