7/30/2019 Integration and Applications of Integration
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INTEGRATION AND APPLICATIONS OF INTEGRATION
1. Integrate the following set of simple functions(i) dxxx
32 55 [4]
(ii) dxxx 2421 [4]
(iii)
dx
x
x2
72 [4]
2. Evaluate the following integrals:
(i)
45
x1
5e
5x
dx [4]
(ii) dxx1 [4]
(iii)
dxx
x44
3
1
4 [5]
3. Evaluate each of the following integrals
(i)
dxx
x2
3 [5]
(ii)
1
5ex
25
x
dx [4]
(iii) dxxx )5()4( 465 (Hint: Use substitution) [5]
4. Evaluate each of the following integrals
(i) dxxe x 564 24 [5]
(ii)
dxxx
45
5 [4]
(iii) dxxx )5()4( 465 (Hint: Use substitution) [5]
5. Evaluate each of the following integrals:(i)
dxx
xx
3
2 118 [4]
(ii) dxx 7 [4]
(iii) dxx
xex
1 [4]
6. Evaluate each of the following integrals
7/30/2019 Integration and Applications of Integration
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(i)
dxx
xx2
12 [5]
(ii)
dxe
x
x3
5 [4]
(iii) dxxxx )54()5(364 (Hint: Use substitution) [5]
7. (a)Find the area under the curve 24 3 xy and the lines
x 1 and 2x
(b)Find the area above the x -axis bounded by the curve 236 xy and the lines 0x and 3x .(c) Find the area under the curve
y x 2 1 and the lines
x 1 and 3x [4]
(d)Find the area under the curve xxy 22 and the lines
x 1 and 4x
(e) Find the area under the curve y = 3x2 +2x +1 within the intervalx =1 andx = 1. [5](f) Find the area under curve
2
4
xxy , between the linesx = 2 andx = 4.
8. (a) The company also determined that its marginal profit in producing and sellingx units of the3GB flash drive is given by
xxP 06.0240)('
Find the original Profit function given that the company has fixed costs of $100,000.
(b) A company has determined that its marginal cost is given by
205.0)( xxC
Find the Cost function given that the company has fixed costs of $500. [4]
(c) A company has determined that its marginal cost is given by30025.0)( xxC
Find the Cost function given that the company has fixed costs of $2500. [4]
(d) A company has determined that its marginal cost is given by
75.0)( xxC
Find the Cost function given that the company has fixed costs of $1500. [5]
(e) A company has determined that its marginal revenue is given by
2001.0)( xxR
Find the Revenue function given that the company has fixed costs of $5000.
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