Topic6.6 (Part1) Properties of Definite Integrals

Topic 6.6 (Part1) Properties of Definite Integrals

​Think about it...

​Did you interpret the following?

​Ask yourself, what is the question asking me to do?

​All is asking is for the area bounded by the limits.

Try the other two.

Check your work!

​Here is a new graph, what is the question asking you to do? Try it!

Check your work!

​You know you are having fun :D

​Here is the last graph for today. Think about it and work it out!

​Where you looking for the answers? :)
Give it another try!

​Did you get them?

​You did it!

​Let's have some

Quick Review!!!

Multiple Choice

Using the areas of each region given
$$\int_a^df\left(x\right)=$$  

• 6

• 20

• 2

• 24

Multiple Choice

The area under a curve is calculated using which mathematical concept?

• antiderivative

• indefinite integral

• definite integral

• derivative

Multiple Choice

The result of $$\int_0^2\left(x^2-2x+1\right)\ dx$$  is:

• positive

• negative

• zero

Multiple Choice

The shaded AREA in the figure is represented by which of the following integral expressions?

• $$\int_{-1}^2f\left(x\right)\ dx$$  

• $$-\int_2^{-1}f\left(x\right)\ dx$$  

• $$-\int_{-1}^2f\left(x\right)\ dx$$  

• $$\int_{-2}^1f\left(x\right)\ dx$$  

Multiple Select

The shaded AREA (+) shown in the figure can be represented by which of the following integral expressions? (select 2)

• $$\int_0^3f\left(x\right)\ dx$$  

• $$-\int_0^1f\left(x\right)\ dx+\int_1^3f\left(x\right)\ dx$$  

• $$\int_0^1f\left(x\right)\ dx+\int_1^3f\left(x\right)\ dx$$  

• $$\int_1^0f\left(x\right)\ dx+\int_1^3f\left(x\right)\ dx$$  

Multiple Choice

Which definite integral models the area highlighted above?

Multiple Choice

• -1

• -2

• 1/2

• -1/2

Multiple Choice

What statement best describes the Riemann Sum?

• 4 intervals, with heights using middle values

• 4 intervals, with heights using left values

• 5 intervals, with heights using middle values

• 5 intervals, with heights using right values