Open Question: Find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis?
17:15 Publicado por Flechado16
Curve y = x² and line y = 4 intersect at (-2, 4) and (2, 4)
So we integrate from x = -2 to x = 2
So we integrate from x = -2 to x = 2
On this interval, line is above the curve
Each cross section perpendicular to x-axis is shaped like a washer, with
outer radius: R = 4
inner radius: r = x²
We user washer method:
V = p ??2² (R² - r²) dx
V = p ??2² (16 - x4) dx
V = p (16x - x5/5) |?2²
V = p ((32 - 32/5) - (-32 + 32/5))
V = p (64 - 64/5)
V = 256p/5
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