Determine the value of ∫[0 to 1] x eˣ dx using integration by parts.
Determine the value of ∫[0 to 1] x eˣ dx using integration by parts.
- A. e
- B. 1
- C. e - 1
- D. 0
Answer: B) 1
Explanation: Using parts: let u=x, dv=eˣdx. Then du=dx, v=eˣ. Integral is [x eˣ] - ∫eˣ dx = [x eˣ - eˣ]. Evaluating from 0 to 1: (e - e) - (0 - 1) = 1.
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