Exam
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SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Evaluate the integral.
36
dx
1)
x5
1)
Solve the differential equation.
dy
= x e2x
2)
dx
2)
Evaluate the integral.
3)
x e8x dx
3)
4)
x sin 10x dx
4)
Solve the problem.
5) Find the area of the region enclosed by the curve y = x sin x and the x-axis for 4
5 .
x
5)
Evaluate the integral.
6)
7)
y ln 7y dy
8x cos
6)
x
dx
2
7)
Use integration by parts to establish a reduction formula for the integral.
8)
x n ex dx
8)
Solve the problem.
9) Find the area between y = (x - 2)ex and the x-axis from x = 2 to x = 7.
Solve the initial value problem.
dy
= x x - 6 and y = 6 when x = 7
10)
dx
9)
10)
solve for the unknown integral.
11)
e8x cos 5x dx
11)
1
Evaluate the integral
15(y6 + 2y3 + 2)3 (2y5 + 2y2 ) dy
12)
12)
Evaluate the definite integral
1
6 r dr
13)
16 + 3r2
0
13)
Evaluate the integral.
cot5 ( 5x) csc2 (5x) dx
14)
7
15)
16)
14)
cot t csc2 t dt
15)
1
dx
cot (9x - 5)
16)
Evaluate the definite integral
4
5- x
dx
17)
x
1
/2
18)
0
cos x
(3 + 3 sin x)3
17)
dx
18)
Evaluate the integral.
dx
19)
sin2 (5x)
19)
Evaluate the integral
16s3 ds
20)
5 - s4
20)
2