Question

Use the limit process to find the area of the region between the graph of the function and the x-axis over the given interval.
y = 16x [-4, 4]

Answer 1

Respuesta:

$A = 0$

Explicación paso a paso:

$A=\lim_{n\to\infty}\sum_{i=1}^{n}(f(x_{i})){\Delta}x\\</p><p>{\Delta}x=\frac{b-a}{n}\\</p><p>x_{i}=a+i{\Delta}x\\</p><p>f(x)=y=16x;a=-4;b=4\\</p><p>{\Delta}x=\frac{4-(-4)}{n}=\frac{8}{n}\\</p><p>x_{i}=\frac{8i}{n}-4=4(\frac{2i}{n}-1)\\</p><p>f(x_{1})=64(\frac{2i}{n}-1)\\</p><p>A=\lim_{n\to\infty}\sum_{i=1}^{n}(64(\frac{2i}{n}-1))(\frac{8}{n})\\</p><p>A=\lim_{n\to\infty}(\frac{512}{n})\sum_{i=1}^{n}(\frac{2i}{n}-1)\\</p><p>A=\lim_{n\to\infty}(\frac{512}{n})((\frac{2}{n})(\frac{n(n+1)}{2})-n)\\</p><p>A=\lim_{n\to\infty}(\frac{512}{n})=0$