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: 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

Objective: Using definite integral we can quickly calculate the area under a curve from interval a to b. In this exercise, we have to be careful when the area is negative, it is below the x-axis. when we apply the definite integration, our answer will be negative. to combat this, we can flip the interval a-->b into b-->a or multiply the integral by -1.

Objectives Students consider left and right limits- as well as function values- in order to develop an informal and introductory understanding of continuity. Task 1: click here  and complete the task Task 2 : copy the note