# TutWk8.pdf - Week 8 Tutorial Questions Chapter 14.3#s 2 6...

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Week 8 Tutorial Questions Chapter 14.3 #s 2, 6, 23, 24, 26, 28, 29, 30, 34
1024 Chapter 14 / Multiple Integrals QUICK CHECK EXERCISES 14.3 ( See page 1025 for answers. ) 1. The polar region inside the circle r = 2 sin θ and outside the circle r = 1 is a simple polar region given by the inequalities r , θ 2. Let R betheregioninthefirstquadrantenclosedbetweenthe circles x 2 + y 2 = 9 and x 2 + y 2 = 100. Supply the miss- ing limits of integration. R f(r, θ) dA = f(r, θ)r dr dθ 3. Let V be the volume of the solid bounded above by the hemisphere z = 1 r 2 and bounded below by the disk enclosed within the circle r = sin θ . Expressed as a double integral in polar coordinates, V = . 4. Express the iterated integral as a double integral in polar coordinates. 1 1 / 2 x 1 x 2 1 x 2 + y 2 dy dx = EXERCISE SET 14.3 1–6 Evaluate the iterated integral. 1. π/ 2 0 sin θ 0 r cos θ dr dθ 2. π 0 1 + cos θ 0 r dr dθ 3. π/ 2 0 a sin θ 0 r 2 dr dθ 4. π/ 6 0 cos 3 θ 0 r dr dθ 5. π 0 1 sin θ 0 r 2 cos θ dr dθ 6. π/ 2 0 cos θ 0 r 3 dr dθ 7–10 Use a double integral in polar coordinates to find the area of the region described. 7. The region enclosed by the cardioid r = 1 cos θ . 8. The region enclosed by the rose r = sin 2 θ . 9. The region in the first quadrant bounded by r = 1 and r = sin 2 θ , with π / 4 θ π / 2.