WBJEE · Maths · Definite Integration
The value of the integral \(\int_{-1}^{1}\left\{\frac{x^{2013}}{e^{|x|}\left(x^{2}+\cos x\right)}+\frac{1}{e^{|x|}}\right\} d x\) is equal to
- A 0
- B \(1-e^{-1}\)
- C \(2 e^{-1}\)
- D \(2\left(1-e^{-1}\right)\)
Answer & Solution
Correct Answer
(D) \(2\left(1-e^{-1}\right)\)
Step-by-step Solution
Detailed explanation
Let \(\quad I=\int_{-1}^{1}\left\{\frac{x^{2013}}{e^{\mid x\left|(x^{2}+\cos x\right)}}+\frac{1}{e^{|x|}}\right\} d x\) \(\Rightarrow \quad I=\int_{-1}^{1} \frac{x^{2013}}{e^{|x|+\left(x^{2}+\cos x\right)}} d x+\int_{-1}^{1} \frac{1}{e^{|x|}} d x\) Here,…
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