JEE Mains · Maths · STD 12 - 7.1 indefinite integral
If \(\int {{x^5}\,{e^{ - {x^2}}}\,dx\, = \,g\,(x)\,{e^{ - {x^2}}} + \,c,} \) where \(c\) is a constant of integration, then \(g(-1)\) is equal to
- A \(-1\)
- B \(1\)
- C \(-\frac {5}{2}\)
- D \(-\frac {1}{2}\)
Answer & Solution
Correct Answer
(C) \(-\frac {5}{2}\)
Step-by-step Solution
Detailed explanation
\(\text { Let } x^{2}=t \quad 2 x d x=d t\) \(\Rightarrow \frac{1}{2} \int t^{2} \cdot e^{-t} d t\) \(=\frac{1}{2}\left[-t^{2} \cdot e^{-t}+\int 2 t \cdot e^{-t}, d t\right]\)…
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