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Unformatted text preview: this deﬁnite integral. f ( x ) = sin( πx ) x < √ x x ≥ Z 11 f ( x ) d x = Is your answer positive or negative? So, what has more area: one “hump” of the function sin( πx ) , or the area under the square root function from to 1 ? How much bigger is it? Just looking at your picture and thinking in terms of areas, is the function R x1 f ( t ) d t increasing or decreasing at x =1 2 ? at x = 0 ? at x = 1 2 ? Is it changing more rapidly at x = 1 2 or at x = 1 ? 3. Evaluate the integrals: Z 1 e tet e t d t Z 9 1 2√ ω w 2 d ω Which integral is the same as the area under the curve on its given interval?...
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 Spring '08
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 Calculus, Fundamental Theorem Of Calculus, t2 dt, (πx)

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