How to find the Square Unit

Question

Find the area (in square units) of the region under the graph of the function f on the interval [−1, 5]. f(x) = 2x + 6

Answer 1

60 square units,

assuming you mean the area under the line y=2x+6, above y=0

between vertical lines x=-1 and x=5

plot the points (-1,4) and (5,16) and graph the line connecting them

line is y=2x+6

from x =-1 to 5

y goes from y=4 to 16

y=2(-1)+6 =4

y=2(5)+6 = 16

use geometry. The area is the sum of the area of a rectangle and a triangle just above it

the rectangle has area =6 times 4 = 24. the triangle has area = half of 6 times 12 = 72/2 =36

24+36 =60

or use calculus

the line is y=2x+6

integrate to get x^2 +6x

evaluate between -1 and 5

to get: 5^2+6(5) - (-1)^2 - 6(-1) = 55 -1+6 =60

if you get the same answer, solving the problem 2 different ways

odds are good it's correct, with no arithmetic calculation mistakes