1. (10 pts) The length of an 18-foot by 15-foot rectangle is increasing at a rate of 5 ft/sec and the width is decreasing at a rate of 3 ft/sec. The length is 18 feet and the width is 15 feet. How fast is the area changing? 2. (10 pts) Verify that F(x) is the antiderivative of the integrand f(x) and use Part 2 of the Fundamental Theorem to evaluate the definite integral. 3x- dx , F(x) = x+23. (15 pts) Use the change of variable technique to find an antiderivative in terms of x: J 3x dx 1 83 15 +84 ) 13 dx 3x2 dx 2+x 4. (15 pts) Evaluate the following definite integrals: In(3) 0 1+ ex dx J x(1 +x3) dx -1 V1 + 3x dx