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Chapter 5 – The Definite Integral. 5.1 Estimating with Finite Sums. Example Finding Distance Traveled when Velocity Varies. LRAM, MRAM, and RRAM approximations to the area under the graph of y=x 2 from x= 0 to x= 3. p.270 (1-19, 26, 27). 5.2 Definite Integrals.
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5.1 Estimating with Finite Sums Example Finding Distance Traveled when Velocity Varies
LRAM, MRAM, and RRAM approximations to the area under the graph of y=x2 from x=0 to x=3
5.2 Definite Integrals Sigma notation enables us to express a large sum in compact form: Ex) Ex) Ex) Ex)
We have that Upper limit Integral sign Lower limit Variable of Integration Integrand
Example Using the Notation Area Under a Curve
Notes about Area The Integral of a Constant
Ex: Show that the value of Average (Mean) Value
Integral Formulas This is known as the indefinite integral. C is a constant.
p. 290 (1 – 29) odd 19 – 29 note Do (31-35) After 5.4
5.4 Fundamental Theorem of Calculus The Fundamental Theorem of Calculus – Part 1
Find Find a function y = f(x) with derivative That satisfies the condition f(3) = 5.
How to Find Total Area Analytically Find the area of the region between the curve y = 4 – x2, [0, 3] and the x-axis. Look at page 301 example 8.
Use the trapezoidal rule with n = 4 to estimate . Compare with fnint. Ex: An observer measures the outside temperature every hour from noon until midnight, recording the temperatures in the following table. What was the average temperature for the 12-hour period?
Simpson’s Rule Ex: Use Simpson’s rule with n = 4 to approximate