Mathematics: Given a parametric curve {x = 2 cost {y = 4 sint 0 = t = π a. Set up but do NOT evaluate an integral to find the area of the region enclosed by the curve and the x-axis. b. Set up but do NOT evaluate an integral to find the area of the surface obtained by rotating the curve about the x-axis.

Given a parametric curve {x = 2 cost {y = 4 sint

navarreteanamen123

31.07.2021

(a) The area of the region would be given by the integral

$\displaystyle\int_0^\pi y(t)\left|x'(t)\right|\,\mathrm dt = 8 \int_0^\pi \sin^2(t)\,\mathrm dt$

(b) The area of the surface of revolution would be given by

$\displaystyle\int_0^\pi y(t)\sqrt{x'(t)^2+y'(t)^2}\,\mathrm dt = 4\int_0^\pi\sin(t)\sqrt{4\sin^2(t)+16\cos^2(t)}\,\mathrm dt$

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giany

02.03.2021

Step-by-step explanation:

16-4=12 8+4=12 hope it helped

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