2001 AB

# The region r is bounded by the x axis and the x 3 and

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Unformatted text preview: igure above. The region R is bounded by the x-axis and the x 3 and y  tan x . The region S is bounded by graphs of y  2 x 3 and y  tan x . the y-axis and the graphs of y  2 (a) Find the area of R. (b) Find the area of S. (c) Find the volume of the solid generated when S is revolved about the x-axis. Point of intersection 2 x 3  tan x at (A, B )  (0.902155,1.265751) (a) Area R = A ¨0 32 ¨A tan x dx x 3 dx = 0.729 2 or Area R = B ¨0 (2 y )1 / 3 2 x 3 dx 2 x3 tan 1 y dy = 0.729 £ 1 : limits ¦ ¦ ¦ ¦ 3 : ¤ 1 : integrand ¦ ¦ ¦ 1 : answer ¦ ¦ ¥ or Area R = ¨ (b) Area S = 32 0 A ¨0 A ¨0 x3 2 tan x dx = 0.729 tan x dx = 1.160 or 1.161 or Area S = B ¨0 2 ¨B (2 tan 1 y dy y )1/ 3 dy = 1.160 or 1.161 £ 1 : limits ¦ ¦ ¦ ¦ 3 : ¤ 1 : integrand ¦ ¦ ¦ 1 : answer ¦ ¦ ¥ or Area S = 2 ¨0 (2 y )1/ 3 dy B ¨0 (2 y )1/ 3 tan 1 y dy = 1.160 or 1.161 (c) Volume = 3 ¨ A 0 2 x3 2 £ 1 : limits and constant ¦ ¦ ¦ ¦ 3 : ¤ 1 : integrand ¦ ¦ ¦ 1 : answer ¦ ¦ ¥ tan2 x dx = 2.6523 or 8.331 or 8.332 Copyri...
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