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irina1246 [14]
1 year ago
5

Make a sketch of the region and its bounding curves. Find the area of the region. The region inside one leaf of r

Mathematics
1 answer:
Anastaziya [24]1 year ago
4 0

The region inside one leaf of r the area of the region is pi.20.

r =cos5θ

cos5θ =0

5θ=pi/2 ,5θ=3pi/2

θ=pi/10,θ=3pi/10

area of one leaf = ∫[pi/10 to 3pi/10](1/2)r2dθ

= ∫[pi/10 to 3pi/10](1/2)(cos5θ)2dθ

= ∫[pi/10 to 3pi/10](1/4)(1+cos10θ)dθ

=[pi/10 to 3pi/10](1/4)(θ+ (1/10)sin10θ)

=(1/4)((3pi/10)+ (1/10)sin3pi) -(1/4)((pi/10)+ (1/10)sinpi)

=(1/4)(3pi/10)  -(1/4)(pi/10)

=(1/4)(2pi/10)  

=pi/20

area of one leaf =pi.20.

Region area (calculus) Region area. The non-negative function given by y = f(x) represents a smooth curve on the closed interval [a, b].The area through the curve of f(x), the x-axis, and the perpendicular lines x = a and x = b The bounding region shown in Figure 1 is given by.

Learn more about the area of the region here: brainly.com/question/19053586

#SPJ4

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