TS EAMCET · Maths · Indefinite Integration
\(\int e^{-x}\left(x^3-2 x^2+3 x-4\right) d x=\)
- A \(-e^{-x}\left(x^3-x^2+5 x-1\right)+\mathrm{c}\)
- B \(e^{-x}\left(x^3-x^2+5 x-1\right)+\mathrm{c}\)
- C \(e^{-x}\left(x^3+x^2+5 x+1\right)+\mathrm{c}\)
- D \(-e^{-x}\left(x^3+x^2+5 x+1\right)+\mathrm{c}\)
Answer & Solution
Correct Answer
(D) \(-e^{-x}\left(x^3+x^2+5 x+1\right)+\mathrm{c}\)
Step-by-step Solution
Detailed explanation
\( \int e^{-x}\left(x^3-2 x^2+3 x-4\right) d x = -e^{-x} \left[ (x^3-2x^2+3x-4) + (3x^2-4x+3) + (6x-4) + 6 \right] + C \) \( = -e^{-x} \left[ x^3 + (-2x^2+3x^2) + (3x-4x+6x) + (-4+3-4+6) \right] + C \) \( = -e^{-x}\left(x^3+x^2+5 x+1\right)+\mathrm{c} \)
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