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General Information Today's Tutoring Tutoring Schedule Tutoring by Topic Q Courses Q Departments Become a Tutor For Students F.A.Q. Tutoring Options Workshops Private Tutors Online Resources Study Groups For Instructors Tutor Talk Request Services Research Miscellaneous Advisory Board Archives UConn Links	Math 1132Q [Hide Descriptions] Functions Inverse of Functions Applet 1 (Inverse of Functions) Integration Integration by Parts Applet 2 (Integration by Parts) Trigonometric Integrals Self Test 1 (Trigonometric Integrals) Trigonometric Substitution Self Test 2 (Trigonometric Substitution) Inproper Integrals Applet 3 (Inproper Integrals) Applications of Integration Area Between Curves Working Example 1 (Area Between 2 Curves with Visualization) : Integrals are used to find the area between two curves. An integral formula is developed and its applicability is discussed in a variety of examples. Applet 4 (Area Between two Curves) Arc Length Working Example 2 (Visualization of the Arclength Integral) Applet 5 (Numerical Approximation + Visualization) : Another illustration of the Riemann Sum modeling method is given, this time to compute the length of a curve in the plane. An integral formula is developed to compute the arc length. It is pointed out that the formula often leads to integrals that must be approximated by numerical methods. Applet 6 (Arc Length) Volumes of Solids of Revolution Applet 7 (A Riemann Sum for a Solid of Revolution) : Integrals find application in many modeling situations involving continuous variables such as area. They allow us to model physical entities that can be described through a process of adding up, or accumulating, smaller infinitesimal parts. In this section, the Riemann Sum approach is used to develop an integral formula for the volume of a solid of revolution. Surfaces of Revolution Working Example 3 (A Surface of Revolution) Working Example 4 (Another Surface of Revolution) Applet 8 (Area of a Surface of Revolution) Numerical Approximations Applet 9 (Trapezoid Rule Visualization) : Many applications of calculus involve definite integrals. If it is possible to find an antiderivative for the integrand, then the integral can be evaluated using the Fundamental Theorem. When an antiderivative is not apparent, numerical (approximate) methods are invoked. The numerical method that is discussed in this section is called the Trapezoid Rule. Work Applet 10 (Work) Expected Value Applet 11 (Expected Value) Sequences and Series Sequences Working Example 5 (Sequences) Convergence Criteria Working Example 6 (Elementary Convergence Tests) Working Example 7 (Integral Test) Working Example 8 (Comparison Test) Working Example 9 (Ratio Test) Alternating Series Working Example 10 (Alternating Series) Power Series Applet 12 (Power Series / Function Plotter) Working Example 11 (Power Series) Taylor Series Applet 13 (Taylor Series Visualizations) Working Example 12 (Taylor Series) Parametric Equations Parametric Equations Working Example 13 (Parametric Equations) Calculus with Parametric Curves Working Example 14 (Calculus with Parametric Curves) Area in Polar Coordinates Working Example 15 (Area in Polar Coordinates)
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