Integral Calculus

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Integration

Welcome!

By completing this course, you are going to be able to determine the integral of any kind of single variable function. Integration basically adds up all the values of a function over an independent variable. The independent variable might be time or any variable of interest. For example, in electronics integrator adds up the charge supplied to it over a time period.

In pure mathematics too, it does the same operation of adding up the value of dependent function over the independent variable over the next few sections we examine some techniques that are frequently successful when seeking antiderivatives of functions.

Sometimes this is a simple problem, since it will be apparent that the function you wish to integrate is a derivative in some straightforward way.

Needless to say, most problems we encounter will not be so simple. Techniques of integration should be clearly understood. Students will have realized the utility of calculus and will have developed technical competence in finding the area under a curve. I hope you will discover that the techniques for integration is not only useful but also intrinsically beautiful.

This course is in three categories.

Category 1 covers basics of Integration, where we discuss

The Definite Integral

2 Evaluating Definite Integrals

3 The Fundamental Theorem of Calculus

4 The Substitution Rule

category 2 covers Techniques of Integration

1 The Indefinite Integral

2 Integration by Parts

3 Trigonometric Integrals and Substitutions

4 Partial Fractions

5 Improper Integrals

and finally category 3 covers Applications of Integration

1 Areas Between Curves

2 Volumes

3 Arc Length

4 Area of a Surface of Revolution

Note: More Practice Exercises is inclusive in this course to better the understanding of various technique of integration

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