A review of integration techniques
We review common techniques to compute indefinite and definite integrals.
Area between curves
We introduce the procedure of “Slice, Approximate, Integrate” and use it study the area of a region between two curves using the definite integral.
We can also use the procedure of “Slice, Approximate, Integrate” to set up integrals to compute volumes.
Solids of revolution
We use the procedure of “Slice, Approximate, Integrate” to compute volumes of solids with radial symmetry.
Length of curves
We can use the procedure of “Slice, Approximate, Integrate” to find the length of curves.
Surface areas of revolution
We compute surface area of a frustrum then use the method of “Slice, Approximate, Integrate” to find areas of surface areas of revolution.
We apply the procedure of “Slice, Approximate, Integrate” to model physical situations.
Integration by parts
We learn a new technique, called integration by parts, to help find antiderivatives of certain types of products by reexamining the product rule for differentiation.
We can use substitution and trigonometric identities to find antiderivatives of certain types of trigonometric functions.
We can use limits to integrate functions on unbounded domains or functions with unbounded range.
Sequences as functions
A sequence can be generated by a function from the integers to the real numbers. There are two ways to establish whether a sequence has a limit.
Slope fields and Euler’s method
We describe numerical and graphical methods for understanding differential equations.
Separable differential equations
Separable differential equations are those in which the dependent and independent variables can be separated on opposite sides of the equation.