a). We can use the equation of a curve in polar coordinates to compute some areas bounded by such curves. The basic approach is the same as with any application of integration: find an approximation that approaches the true value. While doing some experiment, a class of mathematicians came up with a figure with a polar region R, as shown in the figure below. Find the area A of the polar region R. R

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a). We can use the equation of a curve in polar coordinates to compute some areas bounded by such
curves. The basic approach is the same as with any application of integration: find an approximation that
approaches the true value. While doing some experiment, a class of mathematicians came up with a
figure with a polar region R, as shown in the figure below. Find the area A of the polar region R.
R
Transcribed Image Text:a). We can use the equation of a curve in polar coordinates to compute some areas bounded by such curves. The basic approach is the same as with any application of integration: find an approximation that approaches the true value. While doing some experiment, a class of mathematicians came up with a figure with a polar region R, as shown in the figure below. Find the area A of the polar region R. R
d). Use spherical coordinates to find the volume of the solid bounded below by the hemisphere
p=1, z2 0, and above by the cardioid of revolution p=1+cosø. Sketch the region using
Mathematica.
Transcribed Image Text:d). Use spherical coordinates to find the volume of the solid bounded below by the hemisphere p=1, z2 0, and above by the cardioid of revolution p=1+cosø. Sketch the region using Mathematica.
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