Area of the region between the curve y = x2 – 3x and the line y = 3x.

Step-by-step explanation:

To find the domain, find where the curves intersect

x² - 3x = 3x

x² = 6x

x = 0, x = 6

integrate from x = 0 to 6 the difference between the curves

A =∫ 3x - (x² - 3x)dx

A =∫ (6x - x²)dx

A = 3x² - x³/3

A = 3(6)² - (6)³/3 - (3(0)² - (0)³/3)

A = 36 units²

what graph

step-by-step explanation:

18 units²

step-by-step explanation:

first let's find altitude bd using the distance formula

d = √((y₂ - y₁)² + (x₂ - x₁)²)

bd = √((0 - -3)² + (0 - 3)²)

bd = √18

given the placement of points a and c, we can denote that point d bisects segment ac.

we will call ac the base.

using the distance formula

ac = √((0 - 6)² + (-6 - 0)²)

ac = √72

knowing our base and our height, we can plug these into our triangle area formula

area = (b * h)/2

area = (√18 * √72) / 2

area = (√1296) / 2

area = 36 / 2

area = 18 units²