Math 131 C & D
Math 131 A & B 4/18/06
Lab 12: More on the Definite Integral
Part I. The Fundamental Theorem of Calculus.
If r(t) is continuous on [a, b], the [pic] where [pic].
Note that if r(t) is a rate of change then [pic]gives the total change in R(t).
(We will work through example 4 in section 5.3.)
page 274 of text
a. #26 After you write the integral & estimate its value, be sure to check your units.
b. #30
Part II. Review of the definite integral as a limit of Riemann sums.
i) Set up Riemann sums with n rectangles (both RHS & LHS labeling appropriately).
ii) Evaluate the integrals by the definition using your calculator to evaluate the limit.
iii) Interpret the values obtained in (ii) in terms of area.
iv) Check value of your integral with the area interpretation. ((b) will be an estimate.)
a. [pic] b. [pic]
Part III. Use the graph of f to evaluate the definite integrals.
a. [pic]
b. [pic]
c.[pic]
d. [pic]
e. Find the area of the shaded region given that[pic].
f. [pic]
g. Express the total area bounded by the graph of f and the x-axis between x = -4 and x = 3 in terms of definite integrals.
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[pic]
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