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Unformatted text preview: Math 221 Summer 2008 C. Gomez Section 301 Deﬁnite Integrals 1. Express the following limit as a deﬁnite integral:
n P →0 lim 4 − x2 ∆x, i
i=1 where P is a partition of [0, 1]. 2. (a) Sketch the graph of the function f (x) = 3x − 6. 3 (b) Evaluate
2 f (x) dx using the formulas and properties we learned this morning. (c) Check your answer to (b) using area. Turn over! 3. (a) Use the limit of Riemann sums to evaluate
2 (x2 + 1) dx
1 Hint: xi = 1 + 1 i( n ). Why? (b) Check your answer to (a) using the formulas and properties we learned this morning. 2 ...
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