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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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Chapter
Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

(a) Graph the function

f ( x ) = x 2 ln x 1 x 5

(b) Estimate the area under the graph of f using four approximating rectangles and taking the sample points to be (i) right endpoints and (ii) midpoints. In each case sketch the curve and the rectangles.

(c) Improve your estimates in part (b) by using eight rectangles.

(a)

To determine

To draw:The graph for the function f(x)=x2lnx.

Explanation

Given information:

The curve function is f(x)=x2lnx.

The region lies in the interval 1x5. So the limits are a=1 and b=5

(b)

(i)

To determine

The area under the graph of f using right endpoints and four rectangles.

(ii)

To determine

The area under the graph of f using midpoints and four rectangles.

(c)

(i)

To determine

The area under the graph of f using right endpoints and eight rectangles.

(ii)

To determine

The area under the graph of f using midpoints and eight rectangles.

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