C30.8
Demonstrate understanding of indefinite and definite integration:
  • by sight
  • by substitution
  • as used in the Fundamental Theorem of Calculus.

[C, CN, ME, PS, T, V]

Indicators for this outcome
(a)

Distinguish between indefinite and definite integration.

(b)

Critique the statement, “If a function can be differentiated, then it can be integrated.”

(c)

Determine indefinite integrals by sight.

(d)

Determine indefinite integrals by substitution.

(e)

Apply the Fundamental Theorem of Calculus to evaluate definite integrals by sight and by substitution.

(f)

Solve situational questions involving integration.

(g)

Critique the statement, “The integral of $f'(x)dx$ equals $f(x)$.”

(h)

Develop, explain, and apply strategies for determining the area bounded by:

  • a curve and the x-axis over [a,b]
  • two curves.
(i)

Critique the statement, “To integrate any power, we apply in reverse the power rule for differentiation.”

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