**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 =**$\frac{37}{12}$

## 0 comments:

## Post a Comment