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find the upper and lower sums for the region bounded by the graph of the function and the x-axis on the given interval. Leave your answer in terms of n, the number of subintervals.

find the upper and lower sums for the region bounded by the graph of the function and the xaxis on the given interval Leave your answer in terms of n the number class=

Respuesta :

Explanation

The area under a curve between two points can be found by doing a definite integral between the two points

Step 1

a) set the intergral

[tex]\begin{gathered} limits:\text{ 1 and 2} \\ function:\text{ f\lparen x\rparen=6-2x} \end{gathered}[/tex]

hence

[tex]Area=\int_1^26-2x[/tex]

Step 2

evaluate

let ; numbers of intervals

[tex]\begin{gathered} \begin{equation*} \int_1^26-2x \end{equation*} \\ \int_1^26-2x=\lbrack6x-x^2\rbrack=(12-4)-(6-1)=8-5=3 \end{gathered}[/tex]

therefore, the area is

[tex]area=3\text{ units }^2[/tex]

I hope this helps you

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