Solids_with_known_cross_sections
Let's leverage the definite integral to find volumes of figures where we know what their cross sections look like. It is surprisingly fun.
By integrating the difference of two functions, you can find the area between them.
Shell method offers us another way of calculating the volume of solids of revolution. Some solids are more easily found with the shell method.
Rectilinear_motion_integral_calc_
Solve problems about motion along a line using the power of integral calculus. For example, given the velocity of a particle as a function of time v(t), find how much the particle has traveled over a given time period.
The area under a rate function gives the net change. This result of the fundamental theorem of calculus is being put here to use with some real-world problems.
We're used to finding the area under curves in the Cartesian plane, but integration can be used to find area defined by polar curves too.
Washer method is an extension of the Disk method for finding the volumes of more elaborate solids of revolution.
You know how to use definite integrals to find areas under curves. We now take that idea for "spin" by thinking about the volumes of things created when you rotate functions around various lines.
Integral calculus isn't only useful for finding area. For example, it can also be used to find lengths of one-dimensional curves. Learn all about it here.
You may already be familiar with finding arc length of graphs that are defined in terms of rectangular coordinates. We'll now extend our knowledge of arc length to include polar graphs.
We usually calculate the average of N terms by summing them up and dividing by N. How do you find the average of infinitely many terms? For example, the average of a function f(x) for all x-values between 0 and 1? Integral calculus to the rescue!
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