Chapter 4 Integration

Indefinite Integral or Antiderivative

Find the Particular Solution or Solve the Differential Equation

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

1st 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

Using a Right-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) Average Value

Mean Value Theorem Average Value

Find the x value where you get the Average Value

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

2nd Fundamental Theorem of Calculus

Integrate an Even Function

Integrate an Odd Function

U-Substitution or Change of Variables

Find Definite Integral Using U-Substitution or Change of Variables