Question

I'm not sure how to do this:

y = g(x) on [−3, 4] is given by the following curve, which is composed of two line segments and a semicircle:

Answer 1

What is the following curve?

Answer 2

would g(t) be the integral of g(x)?

Answer 3

evaluate by section ... first line from -3 to -1.5
then another line from -1.5 to 0 then semicircle from 0 to 4

Answer 4

g is a function, and t is an independent variable ... i would be same i guess ... if t is plotted along x-axis

Answer 5

they probably mean g(x) , no t is mentioned earlier on..

Answer 6

So, write up the equation to the lines, then take the integral?

Answer 7

its much easier to use the equation of area of circle and area of triangle

Answer 8

and note they are both negative as below x axis

Answer 9

what eigen said. this is a set up for using areas via geometry

Answer 10

(x - h)^2 + (y -k)^2 = r^2 ?

Answer 11

for the semicircle?

Answer 12

pi/2x4

Answer 13

save yourself the work and just do
\[A = \pi r^2\]

Answer 14

although circle equations are awesome

Answer 15

That equation is for a full circle right? So I'd go......pi*2^2 = 4pi--->2pi?

Answer 16

@eigenschmeigen ?

Answer 17

yaa you got it :D

Answer 18

just make sure its negative, because its below y = 0

Answer 19

right, and the other two lines are +/- 1.5x?

Answer 20

yeah, the integral of each line is -1.5 , but using (1/2)(base)(height) we can show that the area of the triangle they make with the x axis is 3. thats how i would approach it anyway, so i think A ?

Answer 21

Yeah, I'd say it's A too. Thanks!

Answer 22

happy to help :)