Exam 16: Methods and Applications of Integration

Determine if converges or diverges.If it converges,to what number does it converge?

Determine if converges or diverges.If it converges,to what number does it converge?

Suppose that the points (-1,2),(-0.5,1),(0,0.5),(0.5,0),and (1,1)lie on the graph of the continuous function f,where f(x)≥ 0.Using Simpson's rule and all of these points,an approximation to the area between the graph of f and the x-axis on the interval is

Suppose that the points (3,2),(3.25,2.5),(3.5,2.25),(3.75,2)and (4,1.5)lie on the graph of the continuous function f,where f(x)≥ 0.Use Simpson's rule and all of the given points to approximate the area between the graph of f and the x-axis on the interval .

A car moves along a straight road in such a way that its velocity in feet/sec is given by v(t)= 3t ,where t is in seconds.Find the average velocity over the first 3 seconds.

Use the table below to determine dx.Indicate the formula number employed. I. + C II. + C III. + C IV. + C

Suppose that the points (1,1),(2,4),and (3,2)lie on the graph of the continuous function f,where f(x)≥ 0.Use the trapezoidal rule and all of the given points to approximate the area between the graph of f and the x-axis on the interval .

If 25% of the initial amount of a radioactive sample remains after 2.5 years,find the decay constant and the half-life of the element.

Use Simpson's rule with n = 4 to estimate the value of

Express the area of the shaded region in terms of an integral (or integrals).Do not evaluate the expression:

Suppose cash reserves (in hundred-thousands of dollars)are approximated by R(x)= 1 + 12x - ,where x is the number of months since the reserve was started.What is the average cash reserve for the first four months?

The exact area of the region bounded by the graphs of y = - 5 and y = 2x + 3 is