Question

The graph of f(x) consists of two straight lines and a semicircle. Use this graph to evaluate (to three decimal places).

Answer 1

28.283
12.000
14.000
34.566
20.283

Answer 2

@iambatman

Answer 3

@Jhannybean

Answer 4

@sammixboo

Answer 5

\[\int_0^2 f(x)dx+\int_2^4f(x)dx\]

Answer 6

I could solve this if I knew what f(x) was.

Answer 7

@Jhannybean

Answer 8

Exactly, I don't know what f(x) is either.

Answer 9

How do I find that out. Or do I not need to?

Answer 10

Butyou could figure it out considering you have a slope and a y intercept (b=0)

Answer 11

the integral is just the area under the curve. You want the integral from 0 to 4 so you can cut that picture any way you want to make the geometry easier.
I would break it into a triangle on the left from 0 to 2, the area of which would be 2*6/2 = 6 units. Then break the integral from 2 to 4 into a triangle on top of a square. The square has an area of 2*2 = 4 units. The triangle above it has an area of 4*2/2 = 4 units as well. So the total area will be 6+4+4 = 14.000 units, so the answer is C

Answer 12

that, OR I suppose you could find the equations of each line and take 2 separate integrals, but there's no need to overcomplicate it

Answer 13

Alright thank you. Also, what would the answer be if it was integral (2,6) instead?

Answer 14

15.142
22.283
12.785
28.283
18.283

Answer 15

Use the same method.

Answer 16

What is the area of a semi circle?

Answer 17

a

Answer 18

A = (pi * r ^ 2) / 2

Answer 19

the format on this site's a bit weird, it wont let me post my explanation

Answer 20

but yeah same thing basically

Answer 21

So the answer is 15.142?

Answer 22

yeah

Answer 23

make sure you understand how to do that

Answer 24

Alright thanks! Also I have one more question, do you think you have time to try it out?

Answer 25

what is it?

Answer 26

From the definition of the definite integral, we have:

Answer 27

You already asked this and @iambatman explained it to you.

Answer 28

Answers:

Answer 29

Yes I know, but I want a second opinion.

Answer 30

Have you tried working it out using his explanation?

Answer 31

@dagrothus

Answer 32

Does this make any sense to you?

Answer 33

yeah i looked at his explanation, he pretty much gives you the answer, just try to understand what he wrote

Answer 34

look back at the definition of an integral

Answer 35

Well I think the answer might be the second one. Is that correct?

Answer 36

ya i think so, but I haven't done this stuff in a while

Answer 37

Alright thank you!