Evaluate the definite integral in Exercise: _ 0 ^ 2 2x dx - Vidyadip

Question

Evaluate the definite integral in Exercise:

$\int\limits_{0}^{\frac{\pi}{2}}\cos2\text{x}\ \text{dx}$

✓

Answer

$\text{Let}\ \text{I}=\int\limits_{0}^{\frac{\text{n}}{2}}\cos2\text{x}\ \text{dx}$

$\int\cos2\text{x}\ \text{dx}=\bigg(\frac{\sin2\text{x}}{2}\bigg)=\text{F}\text{(x)}$

By second fundamental theorem of calculus, we obtain

$\text{I}=\text{F}\bigg(\frac{\pi}{2}\bigg)-\text{F}(0)$

$=\frac{1}{2}\bigg[\sin2\bigg(\frac{\pi}{2}\bigg)-\sin0\bigg]$

$=\frac{1}{2}[\sin\pi-\sin0]$

$=\frac{1}{2}[0-0]=0$

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" 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

If A = {3, 5, 7} and B = {2, 4, 9} and R is a relation given by "is less than", write R as a set ordered pairs.

A fair coin is tossed 8 times, find the probability of.
at least six heads.

Evaluate the following determinant:
$\begin{vmatrix}67&19&21\\39&13&14\\81&24&26 \end{vmatrix}$

Find a matrix X such that 2A + B + X = 0, where.
If $\text{A}=\begin{bmatrix}8&0\\4&-2\\3&6\end{bmatrix}$ and $\text{B}=\begin{bmatrix}2&-2\\4&2\\-5&1\end{bmatrix},$ then find the matrix X of order 3 × 2 such that 2A + 3X = 5B.

Compute the indicated products:
$\begin{bmatrix}1&-2\\2&3\end{bmatrix}\begin{bmatrix}1&2&3\\-3&2&-1\end{bmatrix}$

Find the components along the coordinate axis of the position vector of the following point:

R(-11, -9)

If x and y are connected parametrically by the equations given in Exercise without eliminating the parameter, Find $\frac{\text{dy}}{\text{dx}}.$
$\text{x}=\text{a}\cos\theta,\text{y}=\text{b}\cos\theta$

If $\vec{\text{a}}=3\hat{\text{i}}+4\hat{\text{j}}$ and $\vec{\text{b}}=\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}},$ find the value of $\big|\vec{\text{a}}\times\vec{\text{b}}\big|.$

Find $\frac{d y}{d x}$, if $x^{\frac{2}{3}}+y^{\frac{2}{3}}=a^{\frac{2}{3}}$.

Find $\vec{\text{a}}.\big(\vec{\text{b}}\times\vec{\text{c}}\big), $ if $\vec{\text{a}}=2\hat{\text{i}}+\hat{\text{j}}+3\hat{\text{k}},\vec{\text{b}}=-\hat{\text{i}}+2\hat{\text{j}}+\hat{\text{k}}$ and $\vec{\text{c}}=3\hat{\text{i}}+\hat{\text{j}}+2\hat{\text{k}}$.