WS 5.2 - Intro to Definite Integrals1.pdf - MATH-2211...

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MATH-2211: Calculus of One Variable I Worksheet for section 5.2 Worksheet for Section 5.2 – Definite Integrals Some Properties of Definite Integrals For all properties below, assume that the function f is integrable on the given intervals; k represents a constant. Z a a f ( x ) d x = 0 Z a b f ( x ) d x = - Z b a f ( x ) d x Z c a f ( x ) d x + Z b c f ( x ) d x = Z b a f ( x ) d x Z b a k d x = k ( b - a ) Z b a kf ( x ) d x = k Z b a f ( x ) d x Z b a [ f ( x ) ± g ( x )] d x = Z b a f ( x ) d x ± Z b a g ( x ) d x Practice problems 1. Given that Z 5 3 f ( x ) d x = 6, Z 8 5 f ( x ) d x = 1, and Z 12 8 f ( x ) d x = 7, find each of the following. (a) Z 8 3 f ( x ) d x (b) Z 12 3 f ( x ) d x (c) Z 5 5 f ( x ) d x (d) Z 5 8 f ( x ) d x 2. Given that Z 7 g ( x ) d x = 9, Z 7 g ( x ) d x = - 5, and Z 10 g ( x ) d x = 8, find each of the following.
5. Estimate the area under the graph of f ( x ) = 1 + 2 x 2 from x = 1 to x = 3 using n = 4 rectangles and the:

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