21 lines
460 B
Markdown
21 lines
460 B
Markdown
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### S криволинейной трапеции
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#семестр_1 #высшая_математика
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![[Pasted image 20251216164141.png]]
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$dx\to0$
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$\int aABb=\lim_{ dx \to 0 }\sum\dots=\int_{a}^{b} f(x) \, dx$
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![[Pasted image 20251216164449.png]]
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$x, f(x)=y(t(x))$
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$$
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\begin{array} \\
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t \in [0,1], x(t), y(t) \\
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a(t=0),b(t=1) \\
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l[a,b]=\int_{0}^{1} \sqrt{ \dot{x}^2(t) +\dot{y}^2(t)} \, dx \\
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l=\int_{a}^{b} \sqrt{ 1+(f'(x))^2 } \, dx \\
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\end{array}
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$$
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