Download App

Definite Integrals — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSDefinite Integrals2 Marks
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 "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

Let the relation $R$ be defined on the set $A = \{1, 2, 3, 4, 5\}$ by $R = \{(a, b): |a^2 - b^2| < 8\}.$ Write $R$ as a set of ordered pairs.
→
Write the component of $\vec{\text{b}}$ along $\vec{\text{a}}.$
→
If $\begin{bmatrix}\text{a}+4&3\text{b}\\8&-6 \end{bmatrix}=\begin{bmatrix}2\text{a}+2&\text{b}+2\\8&\text{a}-8\text{b} \end{bmatrix},$ write the value of a - 2b.
→
Prove that the vectors $\vec{a}-2 \vec{b}+3 \vec{c}, 2 \vec{a}+3 \vec{b}-4 \vec{c}$ and $-7 \vec{b}+10 \vec{c}$ are collinear.
→
Evaluate the following integrals:
$\int\limits^1_{-2}\frac{|\text{x}|}{\text{x}}\text{ dx}$
→
Write a unit vector perpendicular to $\hat{\text{i}}+\hat{\text{j}}$ and $\hat{\text{j}}+\hat{\text{k}}.$
→
If the vectors $3\hat{\text{i}}-2\hat{\text{j}}-4\hat{\text{k}}$ and $18\hat{\text{i}}-12\hat{\text{j}}-\text{m}\hat{\text{k}}$ are parallel,  find the value of m.
→
For the matrix $\text{A}=\begin{bmatrix}1&5\\6&7\end{bmatrix}$, verify that
  1. (A + A') is a symmetric matrix.
  2. (A - A') is a skew symmentric matrix.
→
Write the equation of the plane passing through points (a, 0, 0), (0, b, 0) and (0, 0, c).
→
Form the differential equation from the following primitives where constants are arbitrart:$\text{y}=\text{cx}+2\text{c}^2+\text{c}$
→