What is the decimal multiplier to increase by 99%?
2 answers:
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1. Dividing the interval [0, 3] into 6 intervals gives us the partition
[0, 1/2], [1/2, 1], [1, 3/2], ..., [5/2, 3]
Each subinterval has length 1/2. The right endpoints are then
which are given by the sequence
Then the integral is approximated by the Riemann sum,
2. The Riemann sum can be represented by as the sum of the areas of rectangles whose dimensions are determined by the chosen partition and sample points in order to approximate the area between the curve and the
-axis.
3. With subintervals, we get the partition
Each subinterval has length , and the (right-endpoint) Riemann sum is
4. First compute the antiderivative:
Then by the FTC, the definite integral is
5. The integral gives the exact area of the bounded region.