MHT CET · Maths · Indefinite Integration
\(\int \frac{\sin 4 x}{\sin x} \mathrm{~d} x=\) (where \(C\) is a constant of integration.)
- A \(\frac{\sin 3 x}{3}+4 \sin x+C\)
- B \(\frac{1}{3} \sin 3 x-\frac{2}{3} \sin x+C\)
- C \(\frac{2 \sin 3 x}{3}+2 \sin x+C\)
- D \(\frac{2}{3} \sin 3 x-2 \sin x+C\)
Answer & Solution
Correct Answer
(C) \(\frac{2 \sin 3 x}{3}+2 \sin x+C\)
Step-by-step Solution
Detailed explanation
\(\int \frac{\sin 4 x}{\sin x} \mathrm{~d} x=\int \frac{4 \sin x \cdot \cos x \cdot \cos 2 x}{\sin x} \mathrm{~d} x=2 \int 2\) \(\cos x \cdot \cos 2 x d x\)
\(=2 \int\{\cos 3 x+\cos x\} \mathrm{d} x\)
\(=2\left\{\frac{\sin 3 x}{3}+\sin x\right\}+c\)
\(=\frac{2}{3} \sin 3 x+2 \sin x+c\)
\(=2 \int\{\cos 3 x+\cos x\} \mathrm{d} x\)
\(=2\left\{\frac{\sin 3 x}{3}+\sin x\right\}+c\)
\(=\frac{2}{3} \sin 3 x+2 \sin x+c\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The particular solution of the differential equation \(y(1+\log x) \frac{d x}{d y}-x \log x=0\) whenMHT CET 2016 Hard
- The area (in sq. units) bounded by the curves \(y=\sqrt{x}, 2 y-x+3=0, \mathrm{X}\)-axis and lying in the first quadrant isMHT CET 2024 Easy
- \(\int \frac{d x}{\cos 2 x+\sin ^{2} x}=\)MHT CET 2020 Easy
- If a line makes angles of measure \(\frac{\pi}{6}\) and \(\frac{\pi}{3}\) with \(\mathrm{X}\) and Y axes respectively, then the angle made by the line with \(\mathrm{Z}\) axis isMHT CET 2020 Easy
- \((p \wedge q) \vee \sim p\) is equivalent toMHT CET 2010 Easy
- ln \(A B C(a-b)^2 \cos ^2 \frac{C}{2}+(a+b)^2 \sin ^2 \frac{C}{2}=\)MHT CET 2016 Easy
More PYQs from MHT CET
- A spherical balloon is filled with \(4500 \pi\) cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of \(72 \pi\) cubic meters per minute, then the rate (in meters per minute) at which the radius of the balloon decreases 49 minutes after the leakage has begun, isMHT CET 2025 Medium
- A voltmeter of range \(3 \mathrm{~V}\) and resistance \(200 \Omega\) cannot be converted to an ammeter of rangeMHT CET 2011 Medium
- Given below are the two statements.
Statement I: Widow's peak is determined by autosomal dominant gene.
Statement II: Heterozygous individuals have straight hairline.
In the light of above statements, choose the correct answer from the options given below:MHT CET 2024 Hard - Which from following statements is NOT correct regarding tannins?MHT CET 2025 Medium
- Identify 'Z' in the following series of reaction
MHT CET 2020 Hard - A convex lens of focal length ' \(f\) ' produces a real image whose size is ' \(n\) ' times the size of an object. The distance of the object from the lens isMHT CET 2024 Easy