4 x 3 x d x - Vidyadip

Question

$\int \sin 4 x \cos 3 x d x$

✓

Answer

$\text { Let } I =\int \sin 4 x \cdot \cos 3 x d x$
$=\frac{1}{2} \int(2 \sin 4 x \cdot \cos 3 x) d x$
$=\frac{1}{2} \int[\sin (4 x+3 x)+\sin (4 x-3 x)] d x \quad \ldots \ldots[\because 2 \sin A \cos B =\sin ( A + B )+\sin ( A - B )]$
$=\frac{1}{2} \int(\sin 7 x+\sin x) d x$
$=\frac{1}{2}\left[\int \sin 7 x d x+\int \sin x d x\right]$
$=\frac{1}{2}\left(\frac{-\cos 7 x}{7}-\cos x\right)+ c$
$\therefore I =-\frac{1}{14} \cos 7 x-\frac{1}{2} \cos x+ 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 "Solve the Following Question.(2 Marks)" from Question Bank [2022]→Question Bank [2022] — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Solve the following equations by the method of reduction. $x + 3y + 3z = 12, x + 4y + 4z = 15$ and $x + 3y + 4z = 13.$

For each of the following differential equations, find the particular solution satisfying the given condition:

$3 e^x \tan y d x+\left(1+e^x\right) \sec ^2 y d y=0$, when $x=0, y=\pi$

If A is an m × n matrix and B is n × p matrix does AB exist? If yes, write its order.

If $\text{A}=\begin{bmatrix}1\\2\\3\end{bmatrix},$ write $AA^T$.

Construct the truth table for each of the following statement patterns:(p ∧ ~q) ↔ (p → q)

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 $-3,4,2$.

Evaluate the following determinant:
$\begin{vmatrix}\text{x}&-7\\\text{x}&5\text{x}+1 \end{vmatrix}$

A bag contains 7 red, 5 white and 8 black balls. If four balls are drawn one by one with replacement, what is the probability that
none is white?

Construct the truth table for each of the following : [(p ∧ q) ∨ r] ∧ [~r ∨ (p ∧ q)]

Form the differential equation from the following primitives where constants are arbitrart:$\text{y}^2=4\text{ax}$