Question

Consider the function x)-3x+2 Estimate the area between the graph of f and the x axis between x-o and x-3 using six rectangles and right endpoints. Round your answer to two decimal places. Sketch the graph and the rectangles (b) Repeat part (a) using left endpoints. (Round your answer to two decimal places.)

Answer 1

a) First we sketch the graph and the rectangles,

f(x) = 3x + 2

which is a linear equation with y-intercept 2

also at x = 3, f(x) = 3(3) + 2 = 11

which matches the third sketch shown

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Therefore the total area is given as,

A = 0.5 x 3.5 + (0.5 x 5) + (0.5 x 6.5) + (0.5 x 8) + (0.5 x 9.5) + (0.5 x 11)

A = 21.75 sq. units

(b)

First we sketch the graph and the rectangles,

f(x) = 3x + 2

which is a linear equation with y-intercept 2

also at x = 2, f(x) = 3(2) + 2 = 8

which matches the first sketch shown

9 6 14 12 10-64

Therefore the total area is given as,

A = (0.5 x 2) + (0.5 x 3.5) + (0.5 x 5) + (0.5 x 6.5) + (0.5 x 8) + (0.5 x 9.5) =

A = 17.25 sq. units