Total Area vs. Integral

What is the total area beween the curve and the x-axis on the interval $\left[a,d\right]$ ?

• 21

• 13

• 11

• 3

What is the value of  $\int_a^df\left(x\right)dx$  ?

• 21

• 13

• 11

• 3

The total area between the x-axis and the graph of $f\left(x\right)=x-3$  on the interval [0,6] is __________ 0.

• greater than

• less than

• equal to

Which has the largest value?

•  $\int_a^df\left(x\right)dx$  

•  $-\int_a^cf\left(x\right)dx$  

• Total area between curve and x-axis on [a,d]

•  $\int_b^df\left(x\right)dx$  

Which has the smallest value?

•  $\int_a^df\left(x\right)dx$  

•  $-\int_a^cf\left(x\right)dx$  

• Total area between curve and x-axis on [a,d]

•  $\int_b^df\left(x\right)dx$  

What is the total area between the x-axis and the graph of  $f\left(x\right)=6-2x$  on  $\left[0,4\right]$ ?

If  $\int_0^8g\left(x\right)dx=20$  and  $\int_8^{12}g\left(x\right)dx=-5$ then  $\int_0^{12}g\left(x\right)dx=$  

• 25

• 15

• -25

• Impossible to determine

If  $\int_0^8g\left(x\right)dx=20$  and  $\int_8^{12}g\left(x\right)dx=-5$ then the total area between the x-axis and the graph of  $g\left(x\right)$  on the interval  $\left[0,12\right]$  is:

• 25

• 15

• -25

• Impossible to determine

If the graph of the function $y=f\left(x\right)$ is entirely above the x-axis on the interval  $\left[a,b\right]$ , what must be true? (Check all that apply)

•  $\int_a^bf\left(x\right)dx=$  Total Area on  $\left[a,b\right]$  

•  $A\left(x\right)=\int_0^xf\left(t\right)dt$  is an increasing function on  $\left[a,b\right]$  

•  $\int_a^bf\left(x\right)dx$  has a positive value

•  $\int_a^af\left(x\right)dx$  has a positive value

The total area between the x-axis and the graph of $f\left(x\right)=x^2-4$  on the interval $\left[0,4\right]$  is:

•  $0$  

•  $\frac{16}{3}$  

•  $\frac{32}{3}$  

•  $\frac{64}{3}$