SampleProblemsForApplications_Modified_-3 - Integral...

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Integral Calculus MTH 62-141 Problems about Applications 1. Find the area of the region enclosed by the given curves. (a) y = x + 1, y = 9 - x 2 , x = - 1, x (b) y = x , y = x 2 (d) y = 1 + x , y = 3+ x 3 (e) y = 12 - x 2 , y = x 2 - (f) y = x 2 - 4 x , y = 2 x - x 2 . Answer: 9 (g) y = x 3 - x , y = 3 x . Answer: 8 (h) y = tan x , y = 2 sin x , - π/ 3 x π/ 3. Answer: 2 - 2 ln 2 (i) y = x , y = 1 2 x , x = 9. Answer: 59 12 (j) y = 8 - x 2 , y = x 2 , x = - 3, x = 3. Answer: 92 3 (k) x = 2 y 2 , x = 4 + y 2 (l) x = y 2 - 4 y , x = 2 y - y 2 (n) x = e y , x = y 2 - 2, y = 1, y = - (o) y = cos x , y = sin 2 x , x = 0, x = π/ 2. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line (use both disk method and shell method if possible). 3

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