Question

Help with finding areas in graphs. (Calculus)

Answer 1

Are you having trouble with both parts of the question?

Answer 2

Yes

Answer 3

The idea is to partition the domain \([0, \pi]\) and consider the set of the rectangles for that partition. You find the height of the rectangles by taking the value of the function each piece of the partition at some part. For instance you can take the value of the function at the centre of each piece of the partition or the start/end.

Answer 4

how do you do that?

Answer 5

Try finding the length, and height, of the first rectangle.

Answer 6

0.7 and 1?

Answer 7

idk if you need exact values.

Length would be pi/4, height sin(pi/4)

Answer 8

ok

Answer 9

Area is length*height. Then try doing the same with the other rectangles, all the ones on the left are length pi/4. Try finding the heights.

Answer 10

would the heights be sin pi/4 for them also?

Answer 11

No, the heights are found from the right-side... look where the top of the rectangle touches the sinx curve

Answer 12

i see but i don't know which point that is because i don't know the increments the x axis is going up in...

Answer 13

It goes from zero to pi, right? And is divided into 4 sections...

Answer 14

yes

Answer 15

So... you should be able to figure out the increments

Answer 16

0, pi/4, pi/2, 3pi/4?

Answer 17

so it would be pi/4*sin(pi/4), pi/4*sin(pi/2) and pi/4*sin(3pi/4)?

Answer 18

do i add all of those together to find the area of the first??

Answer 19

Yes.

Answer 20

ok :)

Answer 21

should i put the area as a decimal?

Answer 22

Try using exact values. I'm sure you can get the exact value of those sine values...

Answer 23

I don't know what you mean? divide my answer by sine?

Answer 24

do you remember exact values? sin(pi/2) = sqrt(2)/2 etc?

Answer 25

No

Answer 26

This is the answer I got when I did it on my calculator 1.89611889794

Answer 27

You don't remember ever learning exact values of trig functions? I guess you can put them as decimals, just usually you'd use exact values when possible.

Answer 28

ok, how many dp's and what units is this

Answer 29

There aren't units given, so units^2 i guess. And idk, since you may be expected to use exact values.

Answer 30

how can i find the exact value of the decimal then?