Thomas Calculus 13th [Solutions]

356 Chapter 5 Integration
2 2
17. The area of the semicircle is A 1 r 1 (3)
2 2
9
3 2
9 x dx 9 square units
2 3 2
2 2
18. The graph of the quarter circle is A 1 r 1 (4)
4 4
0 2
4 16 x dx 4 square units
4
19. The area of the triangle on the left is A 1 bh
2
1 (2)(2) 2. The area of the triangle on the right is
2
A 1 bh 1 (1)(1) 1 . Then, the total area is 2.5
2 2 2
1
2 | x | dx 2.5 square units
20. The area of the triangle is A 1 1
2 bh 2 (2)(1) 1
1
(1 | x|) dx 1 square unit
1
21. The area of the triangular peak is 1 1 (2)(1) 1.
2 2
The area of the rectangular base is S w (2)(1) 2.
Then the total area is 3
1
(2
1
| x|) dx 3 square
units
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