Chapter 4:
Integration and Integration Techniques
Assignments |
Notes |
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Learning Objectives
Students will be able to:
*approximate the area under the graph of a nonnegative continuous function by using rectangle approximation methods.
*interpret the area under a graph as a net accumulation of a rate of change.
*express the area under a curve as a definite integral and as a limit of Riemann sums.
*compute the area under a curve using a numerical integration procedure.
*apply rules for definite integrals and find the average value of a function over a closed interval.
*apply the Fundamental Theorem of Calculus.
*understand the relationship between the derivative and definite integral as expressed in the Fundamental Theorem of Calculus.
*approximate the definite integral by using the Trapezoidal Rule and estimate the error in using the Trapezoidal Rule.
*approximate the area under the graph of a nonnegative continuous function by using rectangle approximation methods.
*interpret the area under a graph as a net accumulation of a rate of change.
*express the area under a curve as a definite integral and as a limit of Riemann sums.
*compute the area under a curve using a numerical integration procedure.
*apply rules for definite integrals and find the average value of a function over a closed interval.
*apply the Fundamental Theorem of Calculus.
*understand the relationship between the derivative and definite integral as expressed in the Fundamental Theorem of Calculus.
*approximate the definite integral by using the Trapezoidal Rule and estimate the error in using the Trapezoidal Rule.
Vocabulary
area under a curve, average value, bounded function, characteristic function of the rationals, definite integral, differential calculus, dummy variable, error bounds, Fundamental Theorem of Calculus, integrable function, integral calculus, Integral Evaluation Theorem, integral of f from a to b, integral sign, integrand, lower bound, lower limit of integration, LRAM, mean value, Mean Value Theorem for Definite Integrals, MRAM, net area, Rectangular Approximation Method (RAM), Riemann sum, RRAM, sigma notation, subinterval, total area, Trapezoidal Rule, upper bound, upper limit of integration, variable of integration