Evaluate the following integrals: ^ 2 _ - 2 ^2x dx - Vidyadip

Question

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

✓

Answer

$\int\limits^\frac{\pi}{2}_{-\frac{\pi}{2}}\sin^2\text{x}\text{ dx}$$=\int\limits^\frac{\pi}{2}_{-\frac{\pi}{2}}\frac{1-\cos2\text{x}}{2}\text{dx}$
$=\frac{1}{2}\int\limits^\frac{\pi}{2}_{-\frac{\pi}{2}}(1-\cos2\text{x})\text{dx}$
$=\frac{1}{2}\Big[\text{x}-\frac{\sin2\text{x}}{2}\Big]^\frac{\pi}{2}_{-\frac{\pi}{2}}$
$=\frac{1}{2}\Big(\frac{\pi}{2}-0+\frac{\pi}{2}-0\Big)$
$=\frac{\pi}{2}$

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 "Solve the Following Question.(2 Marks)" from Definite Integrals→Definite Integrals — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Find a vector in the direction of $\vec{\text{a}}=2\hat{\text{i}}-\hat{\text{j}}+2\hat{\text{k}}$, which has magnitude of 6 units.

Evaluate $\int\frac{\text{x}^3-1}{\text{x}^2}\text{ dx}$

Find the angle betwwen two vectors $\vec{\text{a}}$ and $\vec{\text{b}}$ if$|\vec{\text{a}}|=3,\big|\vec{\text{b}}\big|=3$ and $\vec{\text{a}}.\vec{\text{b}}=1$

Find the angle between two vectors $\vec{\text{a}}$ and $\vec{\text{b}}$ with magnitudes 1 and 2 respectively and when $\big|\vec{\text{a}}\times\vec{\text{b}}\big|=\sqrt{3.}$

If $\text{P(A)}=\frac{7}{13},\text{P(B)}=\frac{9}{13}$ and $\text{P}(\text{A}\cap\text{B})=\frac{4}{13},$ find $\text{P}\Big(\frac{\text{A}}{\text{B}}\Big).$

Find gof and fog when $f: R \rightarrow R$ and $g: R \rightarrow R$ are defined by:
$f(x)=2 x+x^2$ and $g(x)=x^3$

A bag contains 8 marbles of which 3 are blue and 5 are red. One marble is drawn at random, its cooler is noted and the marble is replaced in the bag. A marble is again drawn from the bag and its colour is noted. Find the probability that the marble will be,
Blue followed by red.

Find the values of x and y if.$\begin{bmatrix}\text{x}+10&\text{y}^2+2\text{y}\\0&-4\end{bmatrix}=\begin{bmatrix}3\text{x}+4&3\\0&\text{y}^2-5\text{y}\end{bmatrix}$

Find the vector equation of line passing through the point having position vector

$5 \hat{i}+4 \hat{j}+3 \hat{k}$ and having direction ratios $-3,4,2$.

If a line is inclined at $60^{\circ}$ and $30^{\circ}$ with the $X$ and $Y$ - axes respectively, then the angle which it makes with $Z$-axis is