Respuesta :
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:
[tex]y= \sqrt{1-x^2}[/tex]
calculating the Δx:
[tex]=\frac{(1 - 0)}{5}\\\\=\frac{1}{5}[/tex]
calculating the Upper sum value:
[tex]=\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[/tex]
calculating the Lower sum value:
Answer:
The upper sum value is 0.8592
The lower sum value is 0.6592.
Step-by-step explanation:
Given information:
The equation [tex]y=\sqrt{1-x^2}[/tex]
And [tex]n=5[/tex]
now, first find derivative of the above equation:
As, [tex]\Delta x=(1/5)\\\Delta x=0.2[/tex]
Now calculate the upper sum value as :
[tex]U=0.2[\sqrt{1-0}+\sqrt{1-0.2^2}+\sqrt{1-0.4^2}+\sqrt{1-0.6^2}]+ \sqrt{1-0.8^2}\\U=0.2\times 4.296\\U=0.8592\\[/tex]
Hence, the upper sum value is 0.8592
Now ,calculate the lower sum value as:
[tex]L=0.2[\sqrt{1-0.2^2}+\sqrt{1-0.4^2}+\sqrt{1-0.6^2}+\sqrt{1-0.8^2}+\sqrt{1-1^2}]\\L= 0.2\times 3.296\\L=0.6592\\[/tex]
Hence, the lower sum value is 0.6592.
For more information visit:
https://brainly.com/question/22983262
