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Chapter 4: Q 17. (page 339)

Each of the sums in Exercises 17鈥�20 approximates the area between the graph of some function f and the x-axis from x = a to x = b. Do some 鈥渞everse engineering鈥� to determine the type of approximation (left sum, midpoint sum, etc.) and identify f(x), a, b, n, 鈭�x, and xk. Then sketch the approximation de-

scribed.

鈭�k=141+k2212

Short Answer

Expert verified

f(x)=x2N=4鈭�x=12xk=1+k2a=1b=3

Step by step solution

01

Step 1. Given information

Function is鈭�k=141+k2212

02

Step 2. Explanation

鈭�k=141+k2212=1+12212+1+22212+1+32212+1+42212

width="87">f(x)=x2N=4鈭�x=12xk=1+k2

Therefore,

a=1b=3

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Most popular questions from this chapter

Prove that 鈭�13(3x+4)dx=20in three different ways:

(a) algebraically, by calculating a limit of Riemann sums;

(b) geometrically, by recognizing the region in question as a trapezoid and calculating its area;

(c) with formulas, by using properties and formulas of definite integrals.

Describe an example that illustrates that 鈭�ab|f(x)|dx is not equal to |鈭�abf(x)dx|.

Given a simple proof that if n is a positive integer and c is any real number, then鈭�k=1nc=cn

Determine which of the limit of sums in Exercises 47鈥�52 are infinite and which are finite. For each limit of sums that is finite, compute its value.

limn鈫�鈭�鈭�k=1nk2+k+1n

Calculate the exact value of each definite integral in Exercises 47鈥�52 by using properties of definite integrals and the formulas in Theorem 4.13.

鈭�06(3x+2)dx
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