Mr Nguyen VCE Maths Methods 12

objective: able to antidifferentiate y=ax^n and y=(ax+b)^n technique: Case 1: 1) add 1 to the power 2) divide it case 2: 1) diff in and divide it 2) anti-diff out

Objective: calculate the period of a tangent function (pi over n). Determine the asymptotes and x-intercepts. Sketch the graphs.

Objective: evaluate the average value of a function note: the average value is the height of a rectangle that has the same area as the area under the curve f(x) from [a,b]

Objective: using integration to evaluate the area between two curves, we need to: 1) solve for the intersection point (x-values) 2) if f(x) is above g(x), we subtract g(x) from f(x) and find the definite integral between [a,b] 3) ignore the negative area, don't have to invert [a,b]-->[b,a] like we did in Ex 11H. The negative areas will cancel out in this case

In this exercise, we will typically be asked to differentiate a function first, and "hence" use the answer to antidifferentiate a complicated function. The trick to do this is to differentiate it correctly, and identify what we can manipulate from dy/dx so that we can apply the integration back to the original function, y.

objective: to find the antidifferentiation of circular functions; the area under the sine, cosine curve. We also need to take into account the area under the x-axis from exercise 11F. NOTE!~!! the antidifferentiation of sine = NEGATIVE cosine!