Fundamental Theorem of Integral Calculus

This course  explores the process of estimating with Riemann sums and trapezoidal approximation methods. Learn how to employ the trapezoid approximation method as opposed to using rectangles via clear illustrations. Before working with sigma notation and its formula, it is important to understand the conversion from rectangular to polar coordinates. This course will take you through the conversion process and the formulas for sums of sequences. It also introduces you to the use of Riemann sums with subintervals to estimate the distance, (in miles) travelled by a particle whose velocity is given. Have you considered using the partition with equal subintervals to estimate the work done? This course analyzes the steps required in finding the area under a curve, as well as the calculus techniques that can be employed to solve ancient problems of calculating complex areas.

If you want to know the use of opposite differentiation or antidifferentiation, as well as how the area of a problem can be solved, then enrol today. You will be able to explain the properties and laws of the definite integral. Also, this course will help you understand the required steps on how the definite integral can be distributed to a sum or difference of functions. Do you know the average value of a function on an interval? The material analyzes the second fundamental theorem of integral calculus and the formula for calculating the average value of a function on an interval. It explains with different examples the formula for calculating the average value of a function on an Interval. If you have struggled with understanding the first fundamental theorem of integral calculus or how to choose uniform partition points, then this course is for you.

You also learn about integration by the u-substitution method together with the substitution equation that can be used to convert Xs to Us. You will be taken through the natural logarithmic functions together with further evidence on the power of a u-substitution technique. See how to reconfigure the integral in terms, as well as the natural exponential functions. Do you know there is a process of differentiating the basic trigonometric functions and finding many integrals involving trigonometric expressions? Get a better understanding of the integration by parts technique that can be used frequently for integrating functions that are described by the product of two functions. This course will explain in detail the concept of the inverse trigonometric functions, as well as the unique value that can be used to make inverse sine a legitimate function. This free online course will be of great interest to calculus students or anyone needing a refresher on definite integrals and methods of integration. Register now and start your next learning math journey today!