I need help evaluating integrals

b) 360

c) -108

d) 72

Step-by-step explanation:

b) from 0 to 30, we have a 2 trapezoids' areas to solve.

trapezoid 1: from 0 to 12

A1 = 144, given by part a

A2 = (6+18)(18)/2 = 216

144 + 216 = 360

c) integral from 30 to 42 is just a triangle whose area will be negative since the y is negative

A = xy/2 = 12(-18)/2 = -108

d)

360-108 + (-18 - 12)(12)/2 = 360-108-180 = 72

r(0,90)(x,y) . t(-5,0)

last option

step-by-step explanation:

∆def to ∆d"e"f"

- rotate 90 counterclockwise degrees

- then translated 5 to the left (x --> x - 5)

answer is the last option

whatvare the choices

step-by-step explanation: