11J: Average value and Straight motion calculus
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]
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11I- The area between two curves
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
11G - integrating circular functions
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!
11F - Finding the area under the curve
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.