Integration Techniques Dominic, Dylan, James

Power Rule for the Indefinite Integral -Don’t forget cookies!

Power Rule for the Indefinite Integral -Don’t forget absolute value!

Indefinite Integral for e and constants -Where b=constant

Integration Formulas for Trig Functions

Try it yourself! 1. 2. 3.

Particular Solutions +C is general solution If given initial condition, we can find particular solution Find f(x) by integrating Insert initial condition to find C Plug C into original f(x)

Try it yourself! 4. Find f(x)

The Definite Integral -Bounded by a and b

Example

Net Area Area under x-axis is considered negative area -

Properties of the Integral

Properties cont.

Properties of Even and Odd Functions

Fundamental Theorem of Calculus, part 1 If f is continuous on [a,b] and F is any antiderivative of f on [a,b] then

Try it yourself! 5.

Average Value Integral/Interval

Try it yourself! 6.

Fundamental Theorem of Calculus, part 2

Examples

Examples cont.

Try it yourself! 7.

Try it yourself! 8. Find LRAM using 5 rectangles

Trapezoidal Rule

Displacement vs Total Distance

U-SUB Opposite of Chain Rule Variable of integration must match variable in expression Substitute value of u back into problem

Example

Try it yourself! 9.

Additional Information Barron’s AP Review Books College Board FRQs Unit 4 Tests/Quizzes Dominic - Presentation Dylan - Quizizz James - 5n1