Question

Let f be the continuous function defined on [−4, 3]
whose graph, consisting of three line segments and a
semicircle centered at the origin, is given above. Let g

Answer 1

\[g(x)=\int\limits_{1}^{x}f(t)dt\]

Answer 2

find g(-2)

Answer 3

@hartnn

Answer 4

Solve this I have a container with 4,200 milliliters of water. How many litres are in my container?

Answer 5

i need to find g(-2)

Answer 6

the equation is the area of a triangle minus the area of a semi circle... do you see that?

Answer 7

the traingle has height = 3 and base = 1, so A(triangle)=1/2 baseXheight = (1/2)(1)(3) = 3/2

Answer 8

the semi circle has area of (1/2)PiR^2 where R=1, That means the area = Pi/2

Answer 9

g(2)

Answer 10

\[\int\limits_{1}^{-2} = -\int\limits_{-2}^{1} \]

Answer 11

yup

Answer 12

i got it thx what about g(2)

Answer 13

usind distance formula?

Answer 14

Im thinking there might be an easier way,

Answer 15

ok

Answer 16

\[(\frac{ -1-1 }{ 3-1 })(1)\] will give you the height of the triangle

Answer 17

how did u get that

Answer 18

then the base is 1

Answer 19

@Edutopia how did u get that ?

Answer 20

@Edutopia

Answer 21

yeah, it should be (-1-0)/(3-1), my mistake: that is the slope which is the change in y with respect to x, so as x change one (the distance between 1 and 2) y will change -1/2

Answer 22

what points did u choose

Answer 23

A(triangle)=(-1/2)(1)(1/2), i used the two given points you have above in your graph

Answer 24

ok

Answer 25

is that same for g'(-3)