TS EAMCET · Maths · Indefinite Integration
If \(\int x^3 \sin 3 x d x=\frac{1}{27}[f(x) \cos 3 x+g(x) \sin 3 x]+\mathrm{c}\) then \(f(1)+g(1)=\)
- A \(14\)
- B \(6\)
- C \(4\)
- D \(12\)
Answer & Solution
Correct Answer
(C) \(4\)
Step-by-step Solution
Detailed explanation
\(\int x^3 \sin 3x dx = -\frac{x^3}{3} \cos 3x + \frac{x^2}{3} \sin 3x + \frac{2x}{9} \cos 3x - \frac{2}{27} \sin 3x + C\) \(= \left(-\frac{x^3}{3} + \frac{2x}{9}\right) \cos 3x + \left(\frac{x^2}{3} - \frac{2}{27}\right) \sin 3x + C\)…
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