Question

Evaluate the integral by interpreting it in terms of areas.

Answer 1

\[\int\limits_{0}^{3} (1/2x-1)dx \]

Answer 2

Is the integrand
A. 1/(2x) - 1
B. 1/(2x -1)
C. (1/2)x - 1
or something else?

Answer 3

C

Answer 4

Sorry I'm new to the typing an equation thing

Answer 5

Good. So it's f(x) = x/2 - 1.

Draw a picture of this and look at what the area is: two triangles.

The question is asking you to evaluate the integral by finding the area of those triangles and then combine them appropriately.

Answer 6

remember that area under the x-axis has a negative sign.

Answer 7

-(1/2)(-1)(1) + (1/2)(1)(1) ?

Answer 8

nope :/

Answer 9

Area right-angled triangle = bh/2,
where b = base, h = height.

Answer 10

Hard to be precise when im drawing lol

Answer 11

i know thats where my (1/2) 1 * 1 came from, it's my drawings really

Answer 12

For the triangle on the right b= 2, h = 1, hence area = (1/2).2.1 = 1. But being under the x-axis, the area = -1.

Now find the area of the other triangle.

Answer 13

okay so (1/2) * (1/2) * 1 = 1/4

so -1+(1/4) = 3/4

Answer 14

negative *

Answer 15

correct, -3/4

Answer 16

my drawings need to improve! thanks!