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f(t) dt where f(t)= Consider the function B defined by the rule B(r) 11 6-2t. 1. Compute B(1) and B(2) exactly 2. Use the first Fundamental Theorem of Calculus to find a formula for B(r) that does not involve integrals. That is, use the first FTC to evaluate (G-21) dt. 3. Ohserve that f is a linear function: what kind of function is B? 4. Using the formula that you found in part (b) that does not involve inte- grals. compute B' (r). 5. While we have defined f by the rule f(t) 6- 2f., it is equivalant to say that fis given by the rule f(r) = 6-2.r. What do you observe about the relationship between B and f?

f(t) dt where f(t)= Consider the function B defined by the rule B(r) 11 6-2t. 1. Compute B(1) and B(2) exactly 2. Use the first Fundamental Theorem of Calculus to find a formula for B(r) that does not involve integrals. That is, use the first FTC to evaluate (G-21) dt. 3. Ohserve that f is a linear function: what kind of function is B? 4. Using the formula that you found in part (b) that does not involve inte- grals. compute B' (r). 5. While we have defined f by the rule f(t) 6- 2f., it is equivalant to say that fis given by the rule f(r) = 6-2.r. What do you observe about the relationship between B and f?

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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f(t) dt where f(t)= Consider the function B defined by the rule B(r) 11 6-2t. 1. Compute B(1) and B(2) exactly 2. Use the first Fundamental Theorem of Calculus to find a formula for B(r) that does not involve integrals. That is, use the first FTC to evaluate (G-21) dt. 3. Ohserve that f is a linear function: what kind of function is B? 4. Using the formula that you found in part (b) that does not involve inte- grals. compute B' (r). 5. While we have defined f by the rule f(t) 6- 2f., it is equivalant to say that fis given by the rule f(r) = 6-2.r. What do you observe about the relationship between B and f?
Transcribed Image Text:f(t) dt where f(t)= Consider the function B defined by the rule B(r) 11 6-2t. 1. Compute B(1) and B(2) exactly 2. Use the first Fundamental Theorem of Calculus to find a formula for B(r) that does not involve integrals. That is, use the first FTC to evaluate (G-21) dt. 3. Ohserve that f is a linear function: what kind of function is B? 4. Using the formula that you found in part (b) that does not involve inte- grals. compute B' (r). 5. While we have defined f by the rule f(t) 6- 2f., it is equivalant to say that fis given by the rule f(r) = 6-2.r. What do you observe about the relationship between B and f?
Expert Solution
Step 1

Given f(x)=6-2t, the fuction B(x) is defined by

B(x)=f(t)dt
Step 2

B(1) and B(2) can be evaluated as

1 B(1)- f)di-j(6-2t)dt - [6r--0 __ = 2 2 B(2)-5)d[(6-21) d - [r-f[6(2)-(2)]6)-(]3 =6t = 1
Step 3

If F'(t)=f(t),then by Fundamental theorem of calculus, we have

t)=F(b)-F(a) a
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