Based on the graph f(t) (attached in the link bellow) fill out approximate yhe values in the table of A(x)= ʃ(superscript x)(subscript 0) f(t) dt.
Based on the graph f(t) attached to this link (http://s19.postimage.org/bjz86zm0j/calc_hw_23_3_graph.png ),
(a) fill out approximate values in the table of:
A(x)= ʃ(superscript x)(subscript 0) f(t) dt.
(The link to this table is: http://s19.postimage.org/mv1vvcsvn/calc_hw_23_3_table.png )
The only exact value of `A(x)` that we can calculate is `A(0)` since there is no area. For the rest of the table we need to use approximations to find the area using rectangles or triangles as necessary.
For `A(1)`, we see that the area under the curve is approximately a rectangle, that goes from x=0 to x=1 and has a height of 1 and base of 1, so `A(1)=0.5`.
The next cell in the table `A(2)` has a positive area and an equal amount of negative area below the x-axis, so `A(2)=0`.
For `A(2.75)`, we need to add an additional negative triangular area with base 0.75 and negative height 1, so `A(2.75)=-0.375`.
`A(3)` adds a small positive area to `A(2.75)`. In this case the triangle has a base of 0.25 and height of 0.75 to get a total area of `A(3)=-0.375+0.1875=-0.1875`.
Finally `A(4)`, is adding a trapezoidal area to `A(3)`. The left height is 0.75, the right height is 5 and the base is 1. This means that `A(4)=-0.1875+2.875=2.6875`.