AP Calculus ABhardmcq1 pt
The integral ∫₀¹ x·eˣ dx equals:
A.e - 1
B.1 - e
C.e
D.1
Explanation
Core Concept
Using integration by parts: u = x, dv = eˣdx. Then du = dx, v = eˣ. ∫x·eˣdx = xeˣ - ∫eˣdx = xeˣ - eˣ + C. Evaluating [0,1]: (1·e - e) - (0 - 1) = 0 + 1 = 1.
Correct Answer
D1
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