JEE Mains · Maths · STD 12 - 7.2 definite integral
The value of \(\int_{-1}^{1} x ^{2} e ^{\left[x^{3}\right]} dx ,\) where \([ t ]\) denotes the greatest integer \(\leq t ,\) is
- A \(\frac{e-1}{3 e }\)
- B \(\frac{ e +1}{3}\)
- C \(\frac{ e +1}{3 e }\)
- D \(\frac{1}{3 e }\)
Answer & Solution
Correct Answer
(C) \(\frac{ e +1}{3 e }\)
Step-by-step Solution
Detailed explanation
\(I=\int_{-1}^{1} x^{2} e^{\left[x^{3}\right]} d x\) \(=\int_{-1}^{0} x ^{2} e ^{\left[x^{3}\right]} d x +\int_{0}^{1} x ^{2} e ^{\left[x^{3}\right]} dx\) \(=\int_{-1}^{0} x ^{2} e ^{-1} dx +\int_{0}^{1} x ^{2} e ^{0} dx\)…
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