Calculus 2 Midterm

MA 312 - Section Number _________ Midterm Exam Name___________________________________

Please show all work and submit as a single file scanned document or using Equation Editor.

Evaluate the integral.

1) 5

0 2x2 + x + 2 dx

Use a definite integral to find an expression that represents the area of the region between the given curve and the x-axis on the interval [0, b].

2) y = 12 x2

Evaluate the integral.

3) x4(x5 - 8)4 dx

Solve the differential equation.

4) dy dx

= 9 xy

Use the definite integral to find the area between the x-axis and f(x) over the indicated interval. 5) f(x) = x2 - 6x + 9; [2, 4]

Solve the initial value problem.

6) dy dx

+ xy = 2x; y(0) = 5

Find the area between the curves. 7) y = x, y = x2

1

Evaluate the integral.

8) 23x sin x dx

9) 4

2 6x ln x dx

10) dx

(16 - x2)2

Evaluate the improper integral or state that it is divergent.

11) 0

-

16 ex sin x dx

Find the area or volume.

12) Find the volume of the solid generated by revolving the region under the curve y = 6e-x2 in the first quadrant about the y-axis.

Decide whether or not the function is a probability density function on the indicated interval.

13) f(x) = 4 74

x3; [0, 3]

Find the expected value of the probability density function to the nearest hundredth. 14) f(x) = 3x-4; [1, )

2