Finding the integral of −4f(x) from 0 to 1 using a graph

[kings13]

Homework Statement

http://www.webassign.net/larson/4_03-48.gif

a) integral -4f(x) from [0,1] using that graph

Homework Equations

The Attempt at a Solution

i really have no idea what to do. i understand integrals but not with agraph? what is it asking me?

 

[rock.freak667]

Hint: An integral within an interval is the same as computing the area within that same interval.

 

[kings13]

so from [0,1] it is just 1/2bh? wouldn't that be just 1/2 x -4?

 

[rock.freak667]

so from [0,1] it is just 1/2bh? wouldn't that be just 1/2 x -4?

Numerically, the integral would be -1/2 since the height is at '-1'. So it would be -1/2*-4 I believe.

 

[kings13]

what about from [0,7] with the integral being 8f(x)dx
i did 1/2(7)(1+5)(8) which was wrong. what did i do wrong?

 

[rock.freak667]

For [0,8] , you have

A triangle in [0,1]

a trapezium in [1,6]

a triangle in [6,8]

So you need to compute the areas there and add them up.