8.1 Arc Length and Surface Area Thurs Feb 4 Do Now Find the volume of the solid created by revolving the region bounded by the x-axis, y-axis, and y =

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8.1 Arc Length and Surface Area Thurs Feb 4 Do Now Find the volume of the solid created by revolving the region bounded by the x-axis, y-axis, and y = 4 – x^2 in the first quadrant about the x - axis

Arc Length We can use Riemann sums to help us find the length of a curve using the distance formula:

Arc Length Assume that f’(x) exists and is continuous on [a, b]. Then the arc length S of y = f(x) over [a, b] is

Ex Over the interval [1,3], find the arc length s of the graph of

Ex (CAS) Find the arch length s of y = sin x over [0, pi]

Surface Area We can use arc length and circumference to determine the surface area of a solid of revolution This does not include the 2 circles at each end of the solid

Surface Area Assume f(x) >= 0 and that f’(x) exists and is continuous on [a, b]. Then the surface area S obtained by rotating the graph of f(x) about the x-axis is

Ex Find the surface area S of the surface obtained by rotating the graph of about the x-axis for [1, 3]

Closure Calculate the arc length of y = x^(3/2) over [1, 2] HW: p.471 #