^2bx dx - Vidyadip

Question

$\int\sin^2\text{bx dx}$

✓

Answer

$\int\sin^2\text{bx dx}$
$=\int\Big[\frac{1-\cos2\text{bx}}{2}\Big]\text{dx}$ $\Big[\therefore\sin^2\text{x}=\frac{1-\cos2\text{x}}{2}\Big]$
$=\frac{1}{2}\int(1-\cos2\text{bx})\text{dx}$
$=\frac{1}{2}\Big[\text{x}-\frac{\sin2\text{bx}}{2\text{b}}\Big]+\text{C}$
$=\frac{\text{x}}{2}-\frac{\sin2\text{bx}}{4\text{b}}+\text{C}$

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

Find the value of $\int \frac{x^2-1}{x^2+1} d x$.

If $\text{A}=\begin{bmatrix}2&3\\5&7\end{bmatrix},$ find A + A^T.

Give an example of a relation which is,
Symmetric and transitive but not reflexive.

Write the equation of the plane parallel to the YOZ- plane and passing through (-4, 1, 0).

The sum of three numbers is 6. If we multiply third number by 3 and add second number to it, we get 11. By adding first and third numbers, we get double of the second number. Represent it algebraically and find the numbers using matrix method.

The probability distribution of random variable X is given below:

$\text{X}$	$0$	$1$	$2$	$3$
$\text{P}(\text{X})$	$\text{k}$	$\frac{\text{k}}{2}$	$\frac{\text{k}}{4}$	$\frac{\text{k}}{8}$

Determine the value of k.

Integrate the function $\frac{4 x+1}{\sqrt{2 x^{2}+x-3}}$

Find the integral: $\int x^{2}\left(1-\frac{1}{x^{2}}\right) d x$

Let E and F be events with P (E) = $\frac{3}{5}$, P (F) = $\frac{3}{{10}}$ and $P(E \cap F)$ = $\frac{1}{5}$. Are E and F independent?

Evaluate:
$\int\Big(\frac{2\cos^2\text{x}-\cos2\text{x}}{\cos^2\text{x}}\Big)\text{dx}$