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面积 2y=5sqrt(x),y=3,2y+2x=7

解答

面积

2 y = 5 x, y = 3, 2 y + 2 x = 7

解答

\frac{139}{600}

+1

十进制

0.23166 \dots

求解步骤

对于

2 y = 5 x

将

y

移到一边:

y = \frac{5 x}{2}

对于

2 y + 2 x = 7

将

y

移到一边:

y = \frac{7 - 2 x}{2}

f_{1} (x) = \frac{5 x}{2}

f_{2} (x) = 3

要找到相交点，解

f_{i} (x) = f_{j} (x)

\frac{5 x}{2} = 3 : x = \frac{36}{25}

\frac{5 x}{2} = \frac{7 - 2 x}{2} : x = 1

3 = \frac{7 - 2 x}{2} : x = \frac{1}{2}

= \int_{\frac{1}{2}}^{1} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{1}^{\frac{36}{25}} ∣ f_{1} (x) - f_{2} (x) ∣ d x

= \int_{\frac{1}{2}}^{1} 3 - \frac{7 - 2 x}{2} d x + \int_{1}^{\frac{36}{25}} \frac{5 x}{2} - 3 d x

\int_{\frac{1}{2}}^{1} 3 - \frac{7 - 2 x}{2} d x = \frac{1}{8}

\int_{1}^{\frac{36}{25}} \frac{5 x}{2} - 3 d x = \frac{8}{75}

= \frac{1}{8} + \frac{8}{75}

化简

= \frac{139}{600}

作图

流行的例子

integral of x(3^x)

\int x (3^{x}) d x

integral of (x^2+7x+3)^4(2x+7)

\int (x^{2} + 7 x + 3)^{4} (2 x + 7) d x

limit as h approaches 0 of (sin(h))/(6h)

h \to 0 lim (\frac{sin ( h )}{6 h})

derivative of sqrt(7+x)

\frac{d}{d x} (7 + x)

limit as x approaches infinity of 0/(+x)

x \to \infty lim (\frac{0}{+ x})