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Chapter 4: Q. 13 (page 399)

Let fbe the function graphed in Exercise12, and define A(x)=鈭�0xf(t)dtList the following quantities in order from smallest to largest:

Short Answer

Expert verified

The quantities in order from the smallest to the largest is,

A(5)<A(0)<A(-1)<A(-2).

Step by step solution

01

Step 1. Given information

The given graph in Exercise 12is,

02

Step 2. The signed area from x=0 to x=-1 is shown below in shade:

03

Step 3. The signed area from x=0 to x=-2 is shown below in shade.

04

Step 4. The signed area from x=0 to x=5 is shown below in shade.

Clearly, from the above figures it is clear that,

A(5)<A(0)<A(-1)<A(-2).

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Most popular questions from this chapter

Use integration formulas to solve each integral in Exercises 21鈥�62. You may have to use algebra, educated guess and-check, and/or recognize an integrand as the result of a product, quotient, or chain rule calculation. Check each of your answers by differentiating.鈭�x2-3x5-7dx

Use integration formulas to solve each integral in Exercises 21鈥�62. You may have to use algebra, educated guess and-check, and/or recognize an integrand as the result of a product, quotient, or chain rule calculation. Check each of your answers by differentiating .

鈭�x2-1(3x+5)dx

Fill in each of the blanks:

(a) 鈭�x6dx=+C.

(b) is an antiderivative of role="math" localid="1648619282178" x6.

(c) The derivative of is x6.

Construct examples of the thing(s) described in the following. Try to find examples that are different than any in the reading.

(a) A function f for which the signed area between f and the x-axis on [0, 4] is zero, and a different function g for which the absolute area between g and the x-axis on [0, 4] is zero.

(b) A function f whose signed area on [0, 5] is less than its signed area on [0, 3].

(c) A function f whose average value on [鈭�1, 6] is negative while its average rate of change on the same interval is positive.

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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