C.I

Integrals

C.I.1Understand the concept of the integral of a function geometrically, numerically, analytically, and contextually.C.I.1aExplain how the definite integral is used to solve area problems.C.I.1bApproximate definite integrals by calculating Riemann sums using left, right, and mid-point evaluations, and using trapezoidal sums.C.I.1cInterpret the definite integral as a limit of Riemann sums.C.I.1dExplain the relationship between the integral and derivative as expressed in both parts of the Fundamental Theorem of Calculus. Interpret the relationship in terms of rates of change.C.I.2Apply theorems and rules of integration to solve mathematical and real-world problems.C.I.2aApply the Fundamental Theorems of Calculus to solve mathematical and real-world problems.C.I.2bExplain graphically and verbally the properties of the definite integral. Apply these properties to evaluate basic definite integrals.C.I.2cEvaluate integrals using substitution.
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