Chapter 4: Q. 10 (page 398)

Consider the function
$A (x) = {鈭�}_{- 蟺}^{蟺} \cos x d t; B (x) = {鈭�}_{蟺}^{x} \cos x d t$
Explain why their derivatives differ by a constant in three different ways .

Short Answer

Expert verified

The derivative of both function differs by constant $A (x) & B (x)$

The derivative of both function differs by constant showing algebrically $A (x) - B (x)$

The third way is depicting graphically.

Step by step solution

Step 1. Given

The given function is $A (x) = {鈭�}_{- 蟺}^{蟺} \cos x d t; B (x) = {鈭�}_{蟺}^{x} \cos x d t$ $A (x) = {鈭�}_{- 蟺}^{蟺} \cos x d t; B (x) = {鈭�}_{蟺}^{x} \cos x d t$

Step 2. Explaining the first way

The first way is by comparing the derivatives of

A (x) - B (x)

$The derivative of A (x) is A' (x) = cosx The derivative of B (x) is B' (x) = cosx$

The both derivative differs by constant.

Step 3, Explaining the second way (algebriacally)

$A (x) - B (x) = {鈭�}_{- 蟺}^{蟺} \cos x d t - {鈭�}_{x}^{蟺} \cos x d t = {鈭�}_{- 蟺}^{蟺} \cos x d t It is known that {鈭�}_{- 蟺}^{蟺} \cos x d t i s c o n s \tan t Hence derivative differ by a constant showing algebraically that A (x) - B (x) i s c o n s \tan t$

Step 4. Third way showing graphically

$A (x) - B (x) = {鈭�}_{- 蟺}^{蟺} \cos x d t Which means that it is the signed area under the graph of y = \cos x f r o m x = - 蟺 to x = 蟺$

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91影视

Consider the function
$A (x) = {鈭�}_{- 蟺}^{蟺} \cos x d t; B (x) = {鈭�}_{蟺}^{x} \cos x d t$
Explain why their derivatives differ by a constant in three different ways .

Short Answer

Step by step solution

Step 1. Given

Step 2. Explaining the first way

Step 3, Explaining the second way (algebriacally)

Step 4. Third way showing graphically

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91影视

Consider the functionA(x)=鈭�-蟺蟺cosxdt;B(x)=鈭�蟺xcosxdtExplain why their derivatives differ by a constant in three different ways .

Short Answer

Step by step solution

Step 1. Given

Step 2. Explaining the first way

Step 3, Explaining the second way (algebriacally)

Step 4. Third way showing graphically

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Discrete Mathematics

Probability and Statistics

Logic and Functions

Applied Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Consider the function
$A (x) = {鈭�}_{- 蟺}^{蟺} \cos x d t; B (x) = {鈭�}_{蟺}^{x} \cos x d t$
Explain why their derivatives differ by a constant in three different ways .