Page 303 - Calculus Demystified

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Fig. S4.6(c) Solutions to Exercises

Fig. S4.6(d)

0 2

3
3
7. (a) Area = −(x + 3x) dx + x + 3xdx
−2 0
4 2 0 4 2 2
x 3x x 3x
= − + + +
4 2 4 2
−2 0
4 2
0 0 (−2) 3 · (−2)
= − − + +
4 2 4 2
4 2
2 3 · 2 0 0
+ + − − = 20.
4 2 4 2
11 (j+1)π/6
j
(b) Area = (−1) sin 3x cos 3xdx
jπ/6
j=−12
11 (j+1)π/6
j 1
= (−1) sin 6xdx
jπ/6 2
j=−12
11 j (j+1)π/6
(−1) cos 6x
= −
2 6
j=−12 jπ/6