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Chapter 4: Q. 3 (page 372)

Approximating with a Riemann sum:

Use a right sum with 10 rectangles to approximate the area under the graph of f(x)=x2 on [0, 5].

Short Answer

Expert verified

The area of the area under the graph f(x)=x2on the interval [0,5] is 48.125.

Step by step solution

01

Step 1. Given Information.

The function:

f(x)=x2on[0,5]

02

Step 2. Graph the function on the graph.

Sketch the graph.

03

Step 3. Find the area.

The area is divided into 10rectangles. so, each rectangle is of length 鈭�x=0.5.

Area, A=f(0.5)鈭�x+f(1)鈭�x+f(1.5)鈭�x+f(2)鈭�x+f(2.5)鈭�x+f(3)鈭�x+f(3.5)鈭�x+f(4)鈭�x+f(4.5)鈭�x+f(5)鈭�x=0.25(0.5)+1(0.5)+2.25(0.5)+4(0.5)+6.25(0.5)+9(0.5)+12.25(0.5)+16(0.5)+20.25(0.5)+25(0.5)=48.125

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Most popular questions from this chapter

Write each expression in Exercises 41鈥�43 in one sigma notation (with some extra terms added to or subtracted from the sum, as necessary).

3鈭�k=225k2+2鈭�kk=224-鈭�k=0251

Given a simple proof that鈭�k=5n(ak+bk)=鈭�k=5nak+鈭�k=5nbk

Describe the intervals on which the function f is positive, negative, increasing and decreasing. Them describe the intervals on which the function A is positive , negative, increasing and decreasing

Consider the region between f and g on [0, 4] as in the

graph next at the left. (a) Draw the rectangles of the left-

sum approximation for the area of this region, with n = 8.

Then (b) express the area of the region with definite

integrals that do not involve absolute values.

Fill in each of the blanks:

(a) 鈭�dx=x6+C.

(b) x6 is an antiderivative of .

(c) The derivative of x6is .
See all solutions

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