Standard 4 : Develop an understanding for and determine integrals.



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General Information

Number: MA.912.C.4
Title: Develop an understanding for and determine integrals.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Grade: 912
Strand: Calculus

Related Benchmarks

This cluster includes the following benchmarks
Code Description
MA.912.C.4.1: Interpret a definite integral as a limit of Riemann sums. Calculate the values of Riemann sums over equal subdivisions using left, right and midpoint evaluation points.
MA.912.C.4.2: Apply Riemann sums, the Trapezoidal Rule and technology to approximate definite integrals of functions represented algebraically, geometrically and by tables of values.
MA.912.C.4.3: Interpret a definite integral of the rate of change of a quantity over an interval as the change of the quantity over the interval.
Clarifications:
Clarification 1: Instruction focuses on the relationshipbegin mathsize 12px style integral subscript a superscript b f apostrophe left parenthesis x right parenthesis d x equals f left parenthesis b right parenthesis minus f left parenthesis a right parenthesis end style which is the Fundamental Theorem of Calculus.
MA.912.C.4.4: Evaluate definite integrals by using the Fundamental Theorem of Calculus.
MA.912.C.4.5: Analyze function graphs by using derivative graphs and the Fundamental Theorem of Calculus.
MA.912.C.4.6:

Evaluate or solve problems using the properties of definite integrals. Properties are limited to the following: 

Equation

MA.912.C.4.7: Evaluate definite and indefinite integrals by using integration by substitution.