TS EAMCET · Maths · Indefinite Integration
\(\int e^{4 x}(\sin 3 x-\cos 3 x) d x=\)
- A \(\frac{e^{4 x}}{25}(7 \sin 3 x-\cos 3 x)+\mathrm{c}\)
- B \(\frac{e^{4 x}}{25}(\sin 3 x-7 \cos 3 x)+\mathrm{c}\)
- C \(\frac{e^{4 x}}{5}(7 \sin 3 x+\cos 3 x)+c\)
- D \(\frac{e^{4 x}}{5}(\sin 3 x+7 \cos 3 x)+c\)
Answer & Solution
Correct Answer
(B) \(\frac{e^{4 x}}{25}(\sin 3 x-7 \cos 3 x)+\mathrm{c}\)
Step-by-step Solution
Detailed explanation
\( \int e^{ax} (P \sin bx + Q \cos bx) dx = \frac{e^{ax}}{a^2+b^2} [ (aP+bQ) \sin bx + (aQ-bP) \cos bx ] + C \) \( a=4, b=3, P=1, Q=-1 \) \( a^2+b^2 = 4^2+3^2 = 16+9 = 25 \) \( aP+bQ = 4(1)+3(-1) = 4-3 = 1 \) \( aQ-bP = 4(-1)-3(1) = -4-3 = -7 \)…
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