Evaluate the following integrals: ^2 _ 0 | |dx - Vidyadip

Question

Evaluate the following integrals:
$\int^\limits{2\pi}_{0}|\sin\text{x}|\text{dx}$

✓

Answer

$\int^\limits{2\pi}_{0}|\sin\text{x}|\text{dx}=\int^\limits{\pi}_{0}\sin\text{x }\text{dx}+\int^\limits{2\pi}_{\pi}-\sin\text{x }\text{dx}$
$=\big[-\cos\text{x}\big]^{\pi}_0+\big[\cos\text{x}\big]^{2\pi}_\pi$
$=\big[1+1\big]+\big[1+1\big]$
$\int^\limits{2\pi}_{0}|\sin\text{x}|\text{dx}=4$

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

For the matrices $, A$ and $B,$ verify that $(AB)\ ' = B\ 'A\ ',$ where $A=\left[\begin{array}{l} {0} \\ {1} \\ {2} \end{array}\right], B=\left[\begin{array}{lll} {1} & {5} & {7} \end{array}\right]$

If $A = [A_{ij}]$ is a $3 \times 3$ scalar matrix such that $a_{11} = 2,$ then write the value of $|A|.$

Find that point on curve $y=x^2-2 x+3$, the tangent drawn on that is parallel to line $2 \mathrm{x}-\mathrm{y}+9=0$.

Form the differential equation from the following primitives where constants are arbitrart:$\text{y}=\text{cx}+2\text{c}^2+\text{c}$

If $|\vec{\text{a}}|=2,\big|\vec{\text{b}}\big|=3$ and $\vec{\text{a}}.\vec{\text{b}}=3,$ find the projection of $\vec{\text{b}}$ on $\vec{\text{a}}.$

If the $\vec{\text{a}}$ and $\vec{\text{b}}$ are such that $|\vec{\text{a}}|=3,\big|\vec{\text{b}}\big|=\frac{2}{3}$ and $\vec{\text{a}}\times\vec{\text{b}}$ is a unit vector, then the angle between $\vec{\text{a}}$ and $\vec{\text{b}}.$

Find the magnitude of two vectors $\vec{a}\ \text{and}\ \vec{b},$ having the same magnitude and such that the angle between them is 60° and their scalar product is $\frac{1}{2}\cdot$

Find the angle between the vectors $\vec{\text{a}} $ and $\vec{\text{b}},$ where$\vec{\text{a}}=\hat {\text{i}}+2\hat{\text{j}}-\hat{\text{k}},$ and $\vec{\text{b}} =\hat{\text{i}}-\hat{\text{j}}+\hat{\text{k}}$

Prove that the determinant $\begin{vmatrix}x&\sin\theta&\cos\theta\\-\sin\theta&-x&1\\\cos\theta&1&x\end{vmatrix}$ is independent of θ.

If $P ( A )=0.6, P ( B )=0.3, P ( A \cap B )=0.2$, then find the value of $P$ (neither $A$ nor $B$ ).