Integration HELPP!! (1 Viewer)

[sky_angel]

We're doing integration now at school and our teacher gave us a question that I can't get. He asked us to integrate y= root (1-x^2) from -1 to 1.

How do I do thisss because he only taught us how to integrate things like 3x^2 or (1+3x)^2.

I asked him if the integral was like the normal one where you add 1 to the power, then put that in the denominator, so I got 2/3 times (1-x^2) root (1-x^2) but he said it was wrong

can someone help me pleeeeaasssee !!

 

[nightweaver066]

Remember what integration helps you find.

*cough* area *cough*

 

[sky_angel]

Remember what integration helps you find.

*cough* area *cough*

oooooohhhhhhhh i remember the teacher told us that we use integration to find the area under the curve. is this curve a circle???

 

[twinklegal19]

oooooohhhhhhhh i remember the teacher told us that we use integration to find the area under the curve. is this curve a circle???

a semi circle to be exact

 

[RealiseNothing]

a semi circle to be exact

a positive semi circle to be even more exact.

 

[sky_angel]

a semi circle to be exact

So can we just use the area of a circle formula? so the area is just pi/2?

 

[nightweaver066]

oooooohhhhhhhh i remember the teacher told us that we use integration to find the area under the curve. is this curve a circle???

Bingo!

Semicircle of radius 1.

Try graph it

 

[nightweaver066]

So can we just use the area of a circle formula? so the area is just pi/2?

Yep

 

[SpiralFlex]

You cannot apply direct numerical integration to this case because the term inside the square root is not linear. You will need to consider the area of the semi-circle to integrate this. But you can also integrate using trigonometric substitution - which would be ineffective in this case.

 

[sky_angel]

Yep

thankss!!! <3

but I don't get why integration finds the area under the curve. Like, how come doing the 'opposite' of differentiation gives us the area? I know that differentiation gives you the gradient but how come if I do it the other way around, I suddenly get area??

 

[twinklegal19]

a positive semi circle to be even more exact.

same thing when it comes to area with the x axis though

So can we just use the area of a circle formula? so the area is just pi/2?

if by that you mean then yes

 

[RealiseNothing]

if by that you mean then yes

m8.

quick edit, solid effort.

 

[sky_angel]

same thing when it comes to area with the x axis though



if by that you mean then yes

but isn't the radius 1 here, so its just pi/2?

 

[deswa1]

thankss!!! <3

but I don't get why integration finds the area under the curve. Like, how come doing the 'opposite' of differentiation gives us the area? I know that differentiation gives you the gradient but how come if I do it the other way around, I suddenly get area??

Has your teacher gone through the idea of the integral as the limiting sum of rectangles under a curve?

 

[RealiseNothing]

but isn't the radius 1 here, so its just pi/2?

Yep.

 

[deswa1]

m8.

quick edit, solid effort.

Yeah- that was solid Twink

 

[sky_angel]

Has your teacher gone through the idea of the integral as the limiting sum of rectangles under a curve?

no... he just told us that we have to find something that if we differentiate, we get the original curve so like the 'opposite' of differentiation. But I don't get why that suddenly gives the area under the curve...

 

[D94]

no... he just told us that we have to find something that if we differentiate, we get the original curve so like the 'opposite' of differentiation. But I don't get why that suddenly gives the area under the curve...

So he hasn't explained it using the Sigma sign and taking small portions, ie. dx, then multiplying them together? Sound familiar?

 

[sky_angel]

So he hasn't explained it using the Sigma sign and taking small portions, ie. dx, then multiplying them together? Sound familiar?

no, but he did tell us to put a dx in the end because you lose marks if you don't

 

[deswa1]

no, but he did tell us to put a dx in the end because you lose marks if you don't

lolwtf. Ok. Get a textbook like Cambridge or look online and actually try to see where integration sorta comes from. This will explain a LOT of things to you