 # Q 13.1.7 3 11/2 0 2ydxdy / 1 3 ydy 1. 0 x²dx = x = 1 3&s...

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Q 13.1.7 3 11/2 0 2ydxdy / 1 3 ydy 1. 0 x²dx = x = 1 3² = (1) 2 3 24 Q 13.1.27 Choose a convenient order. When converted to an iterated integral, the following double integrals are easier to evaluate in one order than the other. Find the best order and evaluate the integral. (y + = {(x,y) : 0 < x 1, - 1 y < 1} (2) R Q 13.1.49 The solid beneath the plane f(x,y) = 24 - 3x - 4y and above the region R = [(x,y) : - -1< x 3, 0 y < 26} f(x,y) = 24 - 3x - 4y Z 24 1 3 2 X y Figure 1: Volume of integration for Q 13.1.49 Q 13.2.21 TT /4 cos x TT /4 cos x dydx = y da - /4 sin x sin x 7/4 /4 = (cosx-sinx)dx= (sinx+cosx) - = - /4 (5) 2 2 /2 2 = + + 2 2 2 2 = 2 = 1.414 Q 13.2.31 Regions of integration Write an iterated integral of a con- tinuous function f over the region R shown in the figure. y 20 (9, 18) y = 2x 10 R y = 3x - 9 4 10 X Figure 2: Region of integration for Q 13.2.31 Q 13.2.40 Evaluating integrals Evaluate the following integrals as they are written.

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