Math 125 Quiz 1 (20 minutes)

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There are three problems in this quiz (the other one is on the back of this page), total of 20 points. Write legibly and show your work fully.

1 Find the most general antiderivative of the function

(a) (4 points) f(x) = x^{1/3} + e^{−3x};

(b) (4 points) g(x) = sin x cos x.

2. (6 points) Find function f such that f′′(x) = −3(x + 1)^{−2} + cos x with f(0) = 1 and f′(0) = 0.

3 Evaluate ∫_{0}^{5}(3 − x) dx by interpreting it in terms of areas.