18.01SC | Fall 2010 | Undergraduate

# Single Variable Calculus

## 4. Techniques of Integration

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### Introduction

This unit covers advanced integration techniques, methods for calculating the length of a curved line or the area of a curved surface, and “polar coordinates” which are an alternative to the Cartesian coordinates most often used to describe positions in the plane.

Part A: Trigonometric Powers, Trigonometric Substitution and Completing the Square

Part B: Partial Fractions, Integration by Parts, Arc Length, and Surface Area

Part C: Parametric Equations and Polar Coordinates

Exam 4

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Congratulations! You’ve made it through Unit 4. Now it’s time to test your knowledge. Begin with the review, and when you’re ready, take the exam. When you’re done, use the included solutions to check your answers.

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This part of the course describes how to integrate trigonometric functions, and how to use trigonometric functions to calculate otherwise intractable integrals.

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Partial Fractions Decomposition and Integration by Parts are techniques for simplifying complex integrals. In this part of the course we also describe how to use integration to find the length of a portion of a graph and the surface area of a rotationally symmetric surface.

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We start by extending our technique for finding the length of a portion of a graph to cover any curve we can describe algebraically. The remainder of this part of the course explores Polar Coordinates, an alternative method of describing locations in the plane.

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## Course Info

Fall 2010
##### Learning Resource Types
Exams with Solutions
Lecture Notes
Lecture Videos
Problem Sets with Solutions
Simulations
Recitation Videos