Question

Use geometry to evaluate [6, -2] f(x) dx where f(x)=

Answer 1

@jim_thompson5910

Answer 2

are you able to graph this?

Answer 3

You can use curly braces to restrict the domain of each piece

https://www.desmos.com/calculator/mk3mcrqrcn

Answer 4

Then the area can be split up into rectangles and triangles

Answer 5

so 3 triangles from (-2,0), (0,2), and (4,6) and a rectangle from (4,6)

Answer 6

triangle area= 0.5bh
triangles (all same dimensions)= 0.5(2)(2)
so 3 triangles with an area of 2, right?

Answer 7

then bh
2*2 = 4
the square has an area of 4

Answer 8

so is the answer
(3*2)+4
6+4=10 ??

Answer 9

Close but the area under the x axis is a negative value (from x = 4 to x = 6)

Answer 10

so its 8?

Answer 11

should be 6

the area under the red curve is 4
the area under the blue curve is 4
4+4 = 8 so far

the area under the green portion is -2

8+(-2) = 6

Answer 12

huh ok

Answer 13

1 more question!