MCQ
$\int \frac{\sin 4 x}{\sin x} d x=$ (Where $C$ is a constant of integration.)
- A
- B
- C
- D
✓
Answer
(c) : Let $I=\int \frac{\sin 4 x}{\sin x} d x$
We know $\sin (A+B)=\sin A \cos B+\cos A \sin B$
So, $\sin (2 x+2 x)=\sin 2 x \cos 2 x+\cos 2 x \sin 2 x$
$
=2 \sin 2 x \cos 2 x=4 \sin x \cos x \cos 2 x
$
$
\begin{aligned}
I=\int & \frac{4 \sin x \cos x \cos 2 x}{\sin x} d x=\int 4 \cos x \cos 2 x d x \\
=\int 2(\cos x+\cos 3 x) d x & =2 \sin x+\frac{2}{3} \sin 3 x+C
\end{aligned}
$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Evaluate: $\int \frac{x^3+x}{x^4-9} d x$
If $\text{y}=\log\sqrt{\tan\text{x}},$ then the value of $\frac{\text{dy}}{\text{dx}}$ at $\text{x}=\frac{\pi}{4}$ is givne by:
→If the current flows through the given circuit, then it is expressed symbolically as,
In $\triangle A B C$, with usual notations, $2 a c \sin \left(\frac{1}{2}(A-B+C)\right)$ is equal to
→The equation of the tangent to the curve $y =1-e^{\frac{x}{2}}$ at the point of intersection with $Y$-axisis
→The position vector of a point $R$ which divides the line joining two points P and Q whose position vectors are $\hat{i}+2\hat{j}- \hat{k}$ and -$\hat{i}+\hat{j}- \hat{k}$ respectively, in the ratio $2: 1$ externally is
→The function $\text{f}(\text{x})=\cot^{-1}\text{x}+\text{x}$ increases in the interval:
→The straight lines represented by the equation $9 x^2-12 x y+4 y^2=0$ are
→$\int_0^{\pi / 4} x \cdot \sec ^2 x d x=$
→The separate equations of the lines represented by $3 x^2-2 \sqrt{3} x y-3 y^2=0$ |are
→