Q. 2C Construct examples of the thing(... [FREE SOLUTION]

Chapter 10: Q. 2C (page 777)

Construct examples of the thing(s) described in the following. Try to find examples that are different than any in the reading:
(a) A function $f$ whose area accumulation function is negative on $[0, 5] .$
(b) A function $f$ whose area accumulation function is decreasing on $[0, 5] .$
(c) Three antiderivatives of $e^{\sin^{2} x} .$

Short Answer

Expert verified

Part (a) The example is $A (5) = {鈭�}_{0}^{5} - t^{2} d t .$

Part (b) The example is $A (5) = {鈭�}_{0}^{5} t^{2} d t .$

Part (c)role="math" localid="1661151675603" $F (x) = {鈭�}_{- 1}^{x} e^{\sin^{2} x} d t, F (x) = {鈭�}_{1}^{x} e^{\sin^{2} x} d t, F (x) = {鈭�}_{2}^{x} e^{\sin^{2} x d t}$

Step by step solution

Part (a) Step 1. Calculation

Let us consider a function on $[0, 5] .$

role="math" localid="1661151518450" $A (5) = {鈭�}_{0}^{5} - t^{2} d t$

Value of the area is negative.

Therefore, the example is $A (5) = {鈭�}_{0}^{5} - t^{2} d t .$

Part (b) Step 1. Calculation

Let us consider a function on $[0, 5] .$

role="math" localid="1661151639470" $A (5) = {鈭�}_{0}^{5} t^{2} d t$

The area accumulation function is decreasing on the interval.

Therefore, the example is $A (5) = {鈭�}_{0}^{5} t^{2} d t .$

Part (c) Step 1. Calculation

The anti derivatives are,

$F (x) = {鈭�}_{- 1}^{x} e^{\sin^{2} x} d t, F (x) = {鈭�}_{1}^{x} e^{\sin^{2} x} d t, F (x) = {鈭�}_{2}^{x} e^{\sin^{2} x d t}$

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Short Answer

Step by step solution

Part (a) Step 1. Calculation

Part (b) Step 1. Calculation

Part (c) Step 1. Calculation

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