COMEDK · Maths · 30. Definite Integration
\(\int_{-1}^{1}\left(x^{27} \cos x+e^{x}\right) d x=\)
- A \(\frac{2 e-1}{e}\)
- B \(\frac{e+1}{e}\)
- C \(e-\frac{1}{e}\)
- D \(\frac{1}{e}\)
Answer & Solution
Correct Answer
(C) \(e-\frac{1}{e}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} \text{Let} \quad I &=\int_{-1}^{1}\left(x^{27} \cos x+e^{x}\right) d x \\ & \Rightarrow \quad I=\int_{-1}^{1} x^{27} \cos x d x+\int_{-1}^{1} e^{x} d x \end{aligned}\) Since, \(f(x)=x^{27} \cos x\) is an odd function.…
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