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Just sketch the parabola and the line. Draw a strip perpendicular to the x axis (parallel to y axis). The length of this strip is one of the sides of the square. You can see that its the y value of the line minus the y value of the parabola. The area of the square will then be (y₁ -...

The sides of the square is y₂ - y₁ *y₂ refers to the parabola *y₁ refers to the line ΔV = (y₁ - y₂)(y₁ - y₂)Δx = (x - x²)(x - x²)dx V = ₀∫¹ (x⁴ -...

Our class has finished analysing BR. The teacher even copied the DVD for everyone in our class to analyse at home.

It is a difficult test. You dont specifically have to be good at maths...imo, its more about "thinking outside the box", so to speak

Following Trev's working out, you should end up with inverse tan

I = INT (e^x cosx) dx Integration by parts needs to be done twice in this question u = e^x dv = cosx.dx du = e^x.dx v = sinx.dx e^x sinx - INT (e^x sinx) dx INT (e^x sinx) dx u = e^x dv = sinx.dx du = e^x.dx v = -cosx.dx -e^x cosx + INT (e^x cosx) dx -e^x cosx...

I also prefer Davin's method. Your school might let 'a' and 'b' be something else When it comes to ellipses, your 'a' is always the bigger number When it comes to hyperbolas, your 'a' is always the first number This ensures the formula you use will always stay the same b^2=a^2(e^2-1)...

Nothing wrong with that. Just dont start getting lazy when the teacher teaches a topic you have already learnt yourself...because i do that :)

Whoops...totally forgot about the change of limits

I think you use slicing Draw x² + y² = a² and dot x = -a/2 and +a/2 Your strip should be between any edge of the circle and x = -a/2 Spin this around the y axis and you should get: Δv = π(x² - a²/4)Δy *x² + y² =...

Our HY wasnt that hard, ended up getting 87%..95% scaled The real average was proly 65%...somehow ended up being 87% scaled

For question one, you split it into 2 sections...the top section should look like an irregular semicircle You should get Δv = π [ (3 - x₁)² - (3 - x₂)² ] Δy *but note x₁ + x₂ = - 3...eliminate either one and you should end up...

Differentiation of log f(x) = f ' (x) / f (x) ---> 1/xlogx

The answer for the first one is 256pi/3 units cubed After i thought about it, do you need to split the slices into 2 sections? hmmm..shell method would be a lot easier

1) Find the volume when the area bounded by y = -x^2 - 3x + 6 and x + y - 3 = 0 is rotated about x = 3 2) The region enclosed by the parts of the line y = x/2, and x = 3, and the part of the hyperbola x^2 - y^2 = 12 is rotated about the y axis. Find the volume

Just a quick question: If the question asked you to find the integral of 2xe^x² are you allowed to go straight to the answer (e^x²), or do you have show stuff, like let u =x²

I've been to the physiotherapist a few times when i had problems with my back. For a short time i was there, i never really saw much other than that massages and the use of that big heating equipment What else is involved apart from massages?

Thx for the info. I guess i could just learn some basic chem off my sister (cos she's yr11 chem next year) if i decide to choose physiotherapy as my 1st preference.. Another question: Would being "physically built up" be some sort of advantage in physiotherapy? When it comes to occupation, is...

I have decided Civil Engineering will be one of my preferences and i am thinking about Physiotherapy as another. Couple of questions: 1) Assumed knowledge - is chemistry really necessary? 2) Run-down of what is to be taught? 3) Employment opportunities?

I am currently in YR12 and i have become increasingly interested in Engineering. My subjects for my HSC include Math MX1&2 and Physics. I have had a general interest in "how things work" and all that construction type stuff since i was little kid and i enjoy the mathematical side of things...So...