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Chapter 4: Q. 28 (page 404)

The algebra of definite integrals:

Fill in the blanks to complete the definite integral rules that follow. You may assume that f and g are integrable functions on [a,b], that c鈭�[a,b], and that k is any real number.

  • 鈭�aaf(x)dx=______.

Short Answer

Expert verified

Ans:鈭�aaf(x)dx=0

Step by step solution

01

Step 1. Given information:

鈭�aaf(x)dx

02

Step 2. Solution:

鈭�aaf(x)dx=鈭�aaf(x)dxIffiscontinuouson[a]andFisanyantiderivativeoff,then=F(x)aa=F(a)-F(a)=0

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Most popular questions from this chapter

Without using absolute values, how many definite integrals would we need in order to calculate the area between the graphs of f(x) = sin x and g(x) = 12on [-蟺2,2蟺] ?

Compare the definitions of the definite and indefinite integrals. List at least three things that are different about these mathematical objects.

Find the sum or quantity without completely expanding or calculating any sums.

Given 鈭�k=14ak=7and,鈭�k=04bk=10,a0=2. Find the value of鈭�k=042ak+3bk.

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

Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals. Use a graph to check your answer.

鈭�蟺/4蟺/2鈥�csc鈦�xcot鈦�xdx
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