Question

The graph of f(x) is shown below. Calculate:

Answer 1

Image has Graph.

Answer 2

integration is area under curve
you have area calculate it to get total area

Answer 3

So the 10, 5 and 30 are what I need to work with?

Answer 4

yes
10 + 5 - 30

Answer 5

Now that I have -15, how can I use this to help me figure out what the original function was?

Answer 6

this is answer for part (a)

Answer 7

@Astrobuoy you don't actually need to find the original function.

Answer 8

Isn't question a) asking for what the f(x) initially was that then if for example f(x)=x^3, was the original I'd put f(x)=2x^2 dx? or am I miss interpreting here?

Answer 9

The way I read it, (a) just asks you to evaluate the integral over 0 to 6. You don't know the function so you can't do integration, but you are just supposed to use your knowledge that integrating gives you area under the curve to evaluate it that way... so (a) evaluates to 5 + 10 - 30 = -15. Whatever that function is, the integral of the function over the region 0 to 6 evaluates to -15.

Answer 10

It will make more sense as you work the rest of them... :)

Answer 11

@Astrobuoy
in this you have to calculate area under curve
no need to find f(x)

Answer 12

In (b), it's the absolute value of that whole expression. So, it says to find the area under the curve, but at the end, express it in absolute terms.

Answer 13

For a) we must know the definite integral of f(x) from 0 to 6,
or in other words the area of the function f(x) from 0 to 6.

We can do this by summing the areas:

From 0 to 2: 10
From 2 to 4: 5
From 4 to 6: -30

Answer 14

(c) is more interesting (finally!!!). You have to look at the absolute value of the curve, and find the area under it. You should get something different from part (a).

Answer 15

For b) we must find