Integration help againn (1 Viewer)

[sky_angel]

I'm trying to finish off Maths hw now because my teacher is checking tomorrow, and I totally forgot about it Can you help me with a few questions? I keep getting the answer wrong but I double checked my answer like a millionnn times but I still keep getting it wrong! Like, even the easiest question in the homework was wrong.

The question asked to find the area under the curve y=x from -1 to 1 so I integrated it with limits -2 and 2, but i keep getting 0!!! even wolfram said 0 but the answer for the homework says the answer is 1. Are the answers wrong???? Please help!!!

 

[sky_angel]

woopsss i meant from -1 to 1. The thing is, for one section of the homework I kept getting it right. Now this section I'm getting them ALL wrong

 

[SpiralFlex]

We integrate like this because we get a negative area if we where to integrate straight out from -1 to 1. This will effective cancel the area out.

Alternatively you can use the area of a triangle from limits 0 to 1 then double! Since the curve is an odd function!

 

[sky_angel]

We integrate like this because we get a negative area if we where to integrate straight out from -1 to 1. This will effective cancel the area out.

thankss :3 but i dont understand the negative area part. how can you have negative area?

 

[SpiralFlex]

thankss :3 but i dont understand the negative area part. how can you have negative area?

You don't. But when we are integrating from -1 to 0, we get a negative area as our answer. Try it out. This is exactly why I have introduced the absolute brackets.

 

[sky_angel]

Why from -1 to 0 gives negative area :S, like why not from 0 to 1 or something? Is it because the limit is minus, so the area is minus?

 

[SpiralFlex]

Graph the curve and shade the boundaries of the limit. Can you now see why?

If the question doesn't ask for the area, then 0 would be your answer as you would compute the integral normally.

 

[nightweaver066]

Why from -1 to 0 gives negative area :S, like why not from 0 to 1 or something? Is it because the limit is minus, so the area is minus?

When you're trying to find the area between -1 to 0, it uses the y-values of the graph. The y-values between -1 to 0 are negative, so you end up with a negative value for the area.

 

[deswa1]

Why from -1 to 0 gives negative area :S, like why not from 0 to 1 or something? Is it because the limit is minus, so the area is minus?

Integration finds the 'positive' area under a curve- essentially the area above the x axis minus the area below the x axis. This is why when you integrated from -1 to 1, you got 0 because the two areas exactly cancelled out.

Between -1 and 0, the curve is below the x axis so the integral will be negative.

 

[sky_angel]

I graphed it and I got two triangles. But I still don't get how you get negative area... it just doesn't make sense.... that's like me saying that there's a negative distance or a negative time.

 

[sky_angel]

Ohhhhhhhh I get it now! Thanks!!! :3 do you mind if I ask a few more questions later if I have problems?

 

[SpiralFlex]

It's why we are awake dear mistress ask away.

 

[deswa1]

It's why we are awake dear mistress ask away.

lol now you sound creepy.

 

[sky_angel]

It's why we are awake dear mistress ask away.

i love youuu <33 you are a life saver

you said something like if the curve is negative then the area is negative too. Does this mean that I can't just find the area without a sketch now? So like do I have to actually sketch all the curves to see where it's negative??

 

[SpiralFlex]

lol now you sound creepy.

I take the head - you take the legs.

 

[SpiralFlex]

i love youuu <33 you are a life saver

you said something like if the curve is negative then the area is negative too. Does this mean that I can't just find the area without a sketch now? So like do I have to actually sketch all the curves to see where it's negative??

Yes I do recommend you start off by sketching the curves. Once you do heaps you can tell!

 

[nightweaver066]

i love youuu <33 you are a life saver

you said something like if the curve is negative then the area is negative too. Does this mean that I can't just find the area without a sketch now? So like do I have to actually sketch all the curves to see where it's negative??

Sketching makes things so much easier.

I generally sketch a quick graph every time i'm finding area/volume.

 

[sky_angel]

I take the head - you take the legs.

ummm okay? That's a little bit scary.... :S

 

[sky_angel]

Sketching makes things so much easier.

I generally sketch a quick graph every time i'm finding area/volume.

okay then, this part will take longer I guess.. how fast can you do them? I've got about 5 left to do, how long would it take you to do that?

 

[enoilgam]

You should always sketch with these things first, so many stupid mistakes are made by NOT laying the ground work before getting into a question.

Just do a quick sketch, it doesnt have to be perfect.