MATA32H3 Lecture 21: The Definite Integral and the Fundamental Theorem of Calculus

1. Consider the definite integral sin (r)d (a) Find an infinite sum that is equal to this definite integral (you do not need to find its value). (b) Use the fundamental theorem of calculus (part 2) to find this definite integral.

Use the Fundamental Theorem of Integral Calculus ("FTIC") an indefinite integral table, and the definition of definite integral to answer the following (a) Compute r3 dr (b) Compute 0 r3 dr -1 (c)From your two answers above, can you guess what the (signed) area under the graph of f(x) = x3 between x =-1 and x = 1 is? If you can't guess it, use a definite integral and the FTIC to compute it. Once you compute the answer, you'll see it

Evaluating a Definite Integral In Exercises 41-46, use the Fundamental Theorem of Calculus to evaluate the definite integral. Use a graphing utility to verify your result. 41.(x - 1) dx 42. (4x* - x) dx 0 43.x^x dx 44.