a)Estimate the area under the graph of f(x) = cos(x) from x = 0 to x = π/2 using four approximating rectangles and right endpoints. Is your estimate an underestimate or an overestimate?
Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
a)Estimate the area under the graph of f(x) = cos(x) from x = 0 to x = π/2 using four approximating rectangles and right endpoints. Is your estimate an underestimate or an overestimate?
Rectangle areas are found by calculating
The width of each rectangle equals
and the height of each rectangle is given by the function value at the right-hand side of the rectangle.
So we must calculate
| 4 | f(xi)Δx = [f(x1) + f(x2) + f(x3) + f(x4)] Δx |
| i = 1 |
where
represent the right-hand endpoints of four equal sub-intervals of
| π |
| 2 |
Since we wish to estimate the area over the interval
| π |
| 2 |
using 4 rectangles of equal widths, then each rectangle will have width
| 4 | f(xi − 1) Δx = [f(x0) + f(x1) + f(x2) + f(x3)]Δx |
| i = 1 |
| π |
| 2 |
Since we wish to estimate the area over the interval
| π |
| 2 |
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