Chapter 6: Q9E (page 362)
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.
(a) Every elementary function has an elementary derivative.
(b) Every elementary function has an elementary anti derivative.
(a) True
(b) False
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Evaluate the integral:\(\int\limits_0^1 {\frac{{{x^3} - 4x - 10}}{{{x^2} - x - 6}}} dx\)
Use a computer algebra system to evaluate the integral. Compare the answer with the result using tables. If the answer is not the same, Show that they are equivalent.
\(\int {{{\sec }^4}xdx} \)
one method of slowing the growth of an insect population without using pesticides is to introduce into the population a number of sterile males that mate with fertile females but produce no offspring. if p represents the number of female insects in a population, s the number of sterile males introduced each generation, and r the population’s natural growth rate, then the female population is related to time t by
\(t = \int {\frac{{p + s}}{{p\left( {(r - 1)p - s} \right)}}} dp\)
Suppose an insect population with 10,000 females grows at a rate of r=0.10 and 900 sterile males are added. Evaluate the integral to the give an equation relating the female population to time.
Evaluate the integral \(\int\limits_0^{\frac{\pi }{2}} {{{\sin }^7}\theta {{\cos }^5}\theta d\theta } \).
Evaluate the integral:\(\int_0^1 {\frac{2}{{2{x^2} + 3x + 1}}} dx\)
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