AP Calc Unit 4: Applications of Integrals

Average value formula

Steps for average value

1) Plug into formula

2) Integrate(antiderivative)

3) Plug in b and a values

4) Subtract and combine!

Second fundamental theorem steps

1)Plug b and a values into “t”

2)Take derivative of these values

3) Bring derivative out in front of everything

Fundamental Theorem

Particular Solution steps

1) Integrate (Antiderivative)

2) Plug in X value into Antiderivative and set equal to y value to find c

3) Write indefinite integral as a definite integral by inputting c value.

Properties of Integrals

Same b and a values: 0

Switched b and a values: -

When do you use long division for integration?

When the numerator is greater than or equal to denominator (same degree and top heavy)

Steps for long division

1) Bring denominator out in front, numerator stays inside

2) Divide

3) Add remainder to actual answer

4)Integrate!