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Chapter 4: Q. 4 (page 384)

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] ?

Short Answer

Expert verified

three

Step by step solution

01

Step1. Given Information

The functions are,

f(x)=sin鈦�x;g(x)=12

The objective is to determine the number of definite integrals would require in order to calculate

the absolute area betweenf(x)=sin鈦�xandg(x)=12on鈭�蟺2,2蟺.

02

Step2. Consider, the following graph

03

Step3. Answer

From the above figure it is clear that 3 intervals are required to calculate the absolute area between fx=sinxand gx=12on -蟺2,2蟺

1st inteval from role="math" localid="1649148607017" -蟺2,0

2nd interval 0,蟺

3rd interval蟺,2蟺

Therefore, the answer is three.

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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. (Hint for Exercise 54: tanx=sinxcosx).

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

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

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