Chapter 1. calc_tutorial_5_7_021

1.1 Problem Statement

{2,3,4,5,6,7,8,9}
pow($a,2)
2*$a
4*$b
2*$b
$m+2
$c*$q
$c*$p

Calculate the integral.

1.2 Step 1

The form of the given indefinite integral resembles the form of .

Thus we should consider a u-substitution that changes to .

Question Sequence

Question 1.1

Such a substitution is

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

Find du.

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Correct.
Incorrect.

1.3 Step 2

Question Sequence

Question 1.2

Substitute and into so that the integrand is rewritten in terms of u only. We will first choose to use the simple algebraic manipulation of multiplying the numerator and denominator of the integrand by x so we can substitute .

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Incorrect. Do you see where you went wrong?
Excellent work.

1.4 Step 3

Question Sequence

Question 1.3

Since is never less than 0, we have . Use this fact to integrate with respect to u. (Use C for the constant of integration.)

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Incorrect. Do you see where you went wrong?
Excellent work.

1.5 Step 4

Question Sequence

Question 1.4

Use the substitution to write in terms of x to calculate the indefinite integral. (Use C for the constant of integration.)

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Incorrect. Do you see where you went wrong?
Excellent work.