9514 1404 393
Answer:
11 7/16
Step-by-step explanation:
The integration resolves into finding the area of two triangles. The left has a height of (-3/8(-2/3)+2) = 2 1/4, and a width of (16/3-(-2/3)) = 6. Then its area is ...
A = (1/2)bh = (1/2)(6)(2 1/4) = 6 3/4
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The right triangle has a height of |(-3/8)(31/3) +2| = |-31/8+16/8| = 15/8. Its width is (31/3) -(16/3) = 5, so its area is ...
A = (1/2)(5)(15/8) = 75/16 = 4 11/16
Then the total area, the value of the integral, is ...
6 3/4 +4 11/16 = 10 23/16 = 11 7/16 . . . the value of the integral
