Math 1425.P70
Examples for 4.1
Name ______________________________________________________
Evaluate.
1)
∫
x15 dx
2)
∫
19 dx
3)
∫
9x7 dx
4)
∫
(5x2 + 1) dx
5)
∫ (8x2 - 3x) dx
6)
∫
(10t2 - 4t - 7) dt
Examples for 4.1
7)
∫ (x - 3)2 dx
8)
∫ (x3 - 5x) dx
9)
∫ (3x8 - 7x3 + 6) dx
10)
∫ 15x-8 dx
11)
∫
61
dx
x
12)
∫
37
dx
x2
13)
∫ 12x3
14)
∫ (x4/3 - 3x5/2) dx
19) f'(x) = x2 + 8, f(3) = 61
x dx
Solve the problem.
20) Find a company's total-cost function if its
15)
marginal cost function is C'(x) = 10x - 7 and
its fixed cost is $12.
∫ 8e4x dx
21) Find a company's total-cost function if its
16)
∫
marginal cost function is C'(x) = 5x2 - 7x + 4
and C(6) = 260.
(x 6 + e3x) dx
Find f such that the given conditions are satisfied.
17) f'(x) = 5x2 - 7x + 4, f(0) = 2
22) A company finds that its marginal revenue
from the sale of the xth unit of its product is
given by R'(x) = 9x 2 - 4. Assuming that
R(0) = 0, find the total-revenue function R.
18) f'(x) = x - 6, f(2) = 0
23) A company has found that its expenditure
rate per day (in hundreds of dollars) on a
certain type of job is given by E'(x) = 10x + 11,
where x is the number of days since the start
of the job. Find the expenditure if the job
takes 6 days.
Math 1425.P70 Examples for 4.1, page 2
Answer Key
Testname: 1425_SECTION4_1
1)
1 16
x +C
16
2) 19x + C
9
3) x8 + C
8
4)
5 3
x +x+C
3
5)
8 3 3 2
x - x +C
3
2
6)
10 3
t - 2t2 - 7t + C
3
7)
1 3
x - 3x2 + 9x + C
3
8)
x4 5x2
+C
4
2
9)
1 9 7 4
x - x + 6x + C
3
4
10) -
15 -7
x +C
7
11) 61 ln x + C
37
12) +C
x
13)
8 9/2
x
+C
3
14)
3 7/3 6 7/2
x
- x
+C
7
7
15) 2e4x + C
x7 e3x
16)
+
+C
7
3
17) f(x) =
5 3 7 2
x - x + 4x + 2
3
2
18) f(x) =
x2
- 6x + 10
2
19) f(x) =
x3
+ 8x + 28
3
20) C(x) = 5x2 - 7x + 12
5
7
21) C(x) = x 3 - x 2 + 4x + 2
3
2
22) R(x) = 3x3 - 4x
23) $24,600
Math 1425.P70 Examples for 4.1, page 3