Questions and answers of find area of region problems.
1-) R is the triangle bounded by the line y = 4 − 3x and the coordinate axes.
Answer = $\frac{8}{3}$
2-) R is the rectangle with vertices (1, 0), (−2, 0), (−2, 5) and (1, 5).
Answer = 15
3-) R is the trapezoid bounded by the lines y = x + 6 and x = 2 and the coordinate axes.
Answer = 14
4-) R is the region bounded by the curve $y = \sqrt{x}$ , the line x = 4, and the x axis.
Answer = $\frac{16}{3}$
5-) R is the region bounded by the curve $y = 4x^3$ , the line x = 2, and the x axis.
Answer = 16
6-) R is the region bounded by the curve $y = 1 − x^2$ and the x axis.
Answer = $\frac{4}{3}$
7-) R is the region bounded by the curve $y = −x^2 − 6x − 5$ and the x axis
Answer = $\frac{32}{3}$
8-) R is the region in the first quadrant bounded by the curve $y = 4 − x^2$ and the lines y = 3x and y = 0.
Answer = $\frac{19}{6}$
9-) R is the region bounded by the curve $y = \sqrt{x}$ and the lines y = 2 − x and y = 0.
Answer = $\frac{7}{6}$
10-) R is the region in the first quadrant that lies under the curve $y = \frac{16}{x}$ and that is bounded by this curve and the lines y = x, y = 0, and x = 8.
Answer = 8(1+ln4)
11-) R is the region bounded by the curve $y = x^2−2x$ and the x axis. (Hint: Reflect the region across the x axis and integrate the corresponding function.)
Answer = $\frac{4}{3}$
12-) R is the region bounded by the curves $y = x^2 + 3$ and $y = 1 − x^2$ between x = −2 and x = 1.
Answer = 12
13-) R is the region bounded by the curve $y = e^x$ and the lines y = 1 and x = 1.
Answer = e-2
14-) R is the region bounded by the curve $y = x^2$ and the line y = x.
Answer = $\frac{1}{6}$
15-) R is the region bounded by the curve $y = x^2$ and the line y = 4.
Answer = $\frac{32}{3}$
16-) R is the region bounded by the curves $y = x^3 − 6x^2$ and $y = −x^2$.
Answer = $\frac{625}{12}$
17-) R is the region bounded by the line y = x and the curve $y = x^3$.
Answer = $\frac{1}{2}$
18-) R is the region in the first quadrant bounded by the curve $y = x^2 + 2$ and the lines y = 11 − 8x and y = 11.
Answer = $\frac{40}{3}$
19-) R is the region bounded by the curves $y = x^2 − 3x + 1$ and $y = −x^2 + 2x + 2$.
Answer = $\frac{11}{8}\sqrt{33}$
20-) R is the region bounded by the curves $y = x^3 − x$ and $y = −x^2 + x$.
Answer = $\frac{37}{12}$
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