# Question #c62e7

##### 3 Answers

The area is bounded by the maroon lines and the blue dots.

#### Explanation:

The area is bounded by the maroon lines and the blue dots.

So we can break down the region into 2 parts:

Note we are interested in the upper region so the area in each case is:

#### Explanation:

Referencing the picture in the other answer, we can split this into two integrals. The first is the region bounded on the interval

#int_-2^0(4-x^2)dx=[4x-x^3/3]_-2^0#

#=[4(0)-0^3/3]-[4(-2)-(-2)^3/3]#

#=0-[-8+8/3]#

#=16/3#

We have to add this value to the amount bounded by

The triangle has a height of

The area of

Here is a third way to find the answer to this question. Rotate your thinking

#### Explanation:

The region is shown below:

We can think of the region as the collection of points whose

Note that the left branch of

On the right it is easy to see that

Our method is analogous to finding an area between

we can integrate with respect to

Greater

"

# = y^2/2+2/3sqrty^3]_0^4#

# = 8 + 16/3 = 40/3#