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The area enclosed by the curve y = f(x) (with f(x) >= 0), the coordinate axes and the line x = x1 equals x1 * e^(x1). Determine f(x).
- e^x
- x e^x
- x e^x - e^x
- x e^x + e^x
Correct answer: x e^x + e^x
Solution
By the fundamental theorem, f(x1) is the derivative of x1 e^(x1), which is e^(x1)(x1+1).
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