Question

Use the upper and lower sums to approximate the area of the region using the given number of subintervals (of equal width). (Round your answers to three decimal places.) y = 1 − x2.

Answer 1

Answer:

The answer to this question can be defined as follows:

The Lower sum ="0.659"

The Upper sum ="0.859"

Step-by-step explanation:

In the given equation there is some mistype error, so the correct equation and its solution can be defined as follows:

Equation:

$y= \sqrt{1-x^2}$

calculating the Δx:

$=\frac{(1 - 0)}{5}\\\\=\frac{1}{5}$

calculating the Upper sum value:

$=\bigtriangleup x \times (f(0) + f(\frac{1}{5}) + f(\frac{2}{5}) + f(\frac{3}{5}) + f(\frac{4}{5})) \\\\= \frac{1}{5} \times (1 + \sqrt{(\frac{24}{25})} + \sqrt{\frac{21}{25}} + \frac{4}{5} + \frac{3}{5})\\\\= 0.859$

calculating the Lower sum value: