Chapter 5 Integration. Indefinite Integral or Antiderivative.

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Presentation transcript:

Chapter 5 Integration

Indefinite Integral or Antiderivative

Find the Particular Solution or Solve the Differential Equation

1.Change into a differential equation. 2.Integrate both sides of the equation. 3.Find c by plugging in the coordinate. 4.Replace c and write the particular solution.

1 st Fundamental Theorem of Calculus Definite Integral or Area Under the Curve on the interval [a,b]

Area below the x-axis is NEGATIVE

Approximate the Area Under a Curve Using a Left-Sided Sum

Approximate the Area Under a Curve Using a Right-Sided Sum

Approximate the Area Under a Curve Using a Midpoint Sum

Midpoint Sum

Approximate the Area Under a Curve Using a Trapezoid Sum

Mean Value Theorem (MVT) or Average Value

Mean Value Theorem Average Value

Find the x value where you get the Average Value

1.Find the Average Value. 2.Set the original function equal to the Average Value. 3.Solve for x.

2 nd Fundamental Theorem of Calculus

0

Integrate an Even Function

Integrate an Odd Function

U-Substitution or Change of Variables

Find Definite Integral Using U-Substitution or Change of Variables