Section 4.7 « Difference Equations to Differential Equations

Section 4.7

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1. Area $\displaystyle{= \int_0^1 (x - x^2)dx = \frac{1}{6}}$

3. Area $\displaystyle{\int_{-1}^2 (x + 2 - x^2)dx = \frac{9}{2}}$

5. Using Newton’s method, and rounding to five decimal places, $r = 0.87673$ is the nonzero solution of the equation $\sin(x) = x^2$ . Hence, rounded to five decimal places,

Area $\displaystyle{= \int_0^r (\sin(x) - x^2)dx = 0.13570}$ .

7. Area $\displaystyle{= \int_0^{\frac{\pi}{4}} (\cos(x) - \sin(x))dx = \sqrt{2} - 1}$

9. (a) Area $\displaystyle{= \int_{-2}^1 (2 - x - x^2)dx}$

(b) Area $\displaystyle{= \int_0^1 2\sqrt{y}dy + \int_1^4 (2 - y + \sqrt{y})dy}$

11. Area $\displaystyle{= \int_{-3}^2 (6 - y - y^2)dy = \frac{125}{6}}$

13. Area $\displaystyle{\int_{-1}^0 (3x^3 - x^4 + 4x^2)dx + \int_0^4 (3x^3 - x^4 + 4x^2)dx}$
$\displaystyle{= \int_{-1}^4(3x^3 - x^4 + 4x^2)dx = \frac{875}{4}}$

14. Area $\approx 178,667$ square yards

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Difference Equations to Differential Equations

Section 4.7

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