Spurlock MAT 230 Chapter 4 Spring 2021
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Find the integral.
1) ? (x6 + e5x) dx
2) The rate at which an assembly line worker’s efficiency E (expressed as a percent) changes with
respect to time t is given by E'(t) = 55 – 6t, where t is the number of hours since the worker’s shift
began. Assuming that E(1) = 92, find E(t).
Approximate the area under the graph of f(x) over the specified interval by dividing the interval into the
indicated number of subintervals and using the left endpoint of each subinterval.
3) f(x) = -0.02×4 – 0.2×2 + 10; interval [-4, 4]; 4 subintervals
x3 + 8
x + 2
5) The time required for workers to produce each unit of a product decreases as the workers become
more familiar with the production procedure. It is determined that the function for the learning
process is T(x) = 2 + 0.3 1
, where T(x) is the time, in hours, required to produce the xth unit.
Find the time required for a new worker to produce units 10 through 15.
Find the area bounded by the given curves. Show all your work to support your answer.
6) y = x2 – 5x + 4, y = -(x – 1)2
Find the average value over the given interval.
7) y = 4x + 2; [3, 7]
Find the integral.
8) ? x2 x3 + 3 dx
9) The rate of growth of profit (in millions) from an invention is approximated by P'(x) = xe-x2
where x represents time in years. The total profit in year 1 that the invention is in operation is
$25,000. Find the total profit function P(x).
Evaluate. Assume u > 0 when ln u appears. Show all your work to support your answer.
10) ? t3 ln (t4 + 2)
t4 + 2
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