Question

1.Sketch the region enclosed by the graphs of each of the following curves, and determine the area of the region enclosed by the graphs of the functions:

y=x^2

y=4x-x^2

2. Find the area between the graph of  and the x axis on the interval [-3, 1].

Answer 1

#1

Given equations:
(Represented as blue)

(Represented as yellow)

Graph:

Area enclosed by the graphs:

Here , and are intersecting points of both the curves

From graph we can see that the intersections are

putting values in the expression we have,

using formula: and , we get

According to our guidelines, if there are multiple questions then we are allowed only to do the first one.

If you need clarification at any step please let me know. Thank you