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Chapter 4: Q. 76 (page 363)

ProveTheobjectiveistoprovethat鈭�kf(x)dx=k鈭�f(x)dxinwords.LetFxbethederivativeoff(x).

Short Answer

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Proved

Step by step solution

01

Step 1. To prove

鈭�kf(x)dx=k鈭�f(x)dx

02

Step 2. Proving

鈭�kf(x)dx=k鈭�f(x)dx=鈭�kf(x)dx=kF'(x)+C=kF'(x)+Ck=鈭�kf(x)dxHenceProved]

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Most popular questions from this chapter

If 鈭�-23f(x)dx=4,鈭�-26f(x)dx=9,鈭�-23g(x)dx=2, and 鈭�36g(x)dx=3, then find the values of each definite integral in Exercises 29-40. If there is not enough information, explain why.

鈭�-2-2x(f(x)+3)2dx

Write out all the integration formulas and rules that we know at this point.

Read the section and make your own summary of the material.

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

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] ?
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