Area Between Curves

Area Between Curves

Let's start today with an integral...
Evaluate

 $\int_{ }^{ }\tan\left(x\right)dx$  using the substitution rule.

Let's Decide

• Two functions exist in this graph.

•  $y=3x^2+2$  and  $y=4x$  

• They are bounded by vertical lines

• What is the area between the curves bounded by these x-values? How did you do it?

Open Ended

 $y=4-x^2$  and $y=-5$  are shown in the graph. At what two x-values to the graphs intersect?

Area between the curves

• How will we set this up?

• What will be the area that is bounded between these two graphs?

Open Ended

 $x=y^2$  and $x=2y$  are graphed on the same two dimensional coordinate grid. At what values will the two graphs cross?

Let's Try it Without a Picture

• From the previous question, which graph is to the right?

• How are we going to set up this integral?