Chapter 1. calc_tutorial_5_6_013

1.1 Problem Statement

{2,3,5}
{7,11,13}
$b+1
$b+2
round((pow($b,3)-pow($a,3))/75+(pow($b,2)-pow($a,2))/2,2)

Determine the indefinite integral. Use substitution.

1.2 Step 1

We use the Substitution Method to evaluate the given indefinite integral. The substitution u = x + 2 was chosen because the composite u$b = (x + $a)$b appears in the integrand.

For

Question Sequence

Question 1.1

Solve for x.

tgPiADA/e+TMPg4exHXjma9tFYPdbqOsTtZ9l7UuDxC6BDKg2S4frSwyDn3IolhpOwcxRN4hHnYQTb8K16zxDSl/kL7ImRbnF0h67bRbC6y+YcU3nb5ecvPBPC3Fi+RtIr95ku4EZjErjps7F+LQpECGICEhJ9m4ilX6Fbp5Q0fDfpxvehJlno8c1w+bPBBPj/Df1MNrtZkqmFdVSlRYjQXEp6RY9/b7MTgA9RPQKdTFklW+hfWCDB5Qj4vC/tm5tSKa+MELJ8lsJiXKVU+DIdUrgnPF5/invDR7wK9JIFQEQmjlnnPslX/qPnOl/xtoD4g4CGYrcs18CQms37Zy8WpAQXQjl27Qolv7Rk6+3Aa+Zg3KfpmI/uG8LQ2vKeReCBY/UGCD90HVh4fmTaF4ZdGxcX6KSoNdaBT8Oc+dxmRP71qfQqq62h1CQtdnLGLOyyECdaY0lic=

Substitute the expressions for u and du to rewrite the integral in terms of u.

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
Correct.
Incorrect.

1.3 Step 2

Question Sequence

Question 1.2

Now evaluate the indefinite integral in terms of u. (Use C for the constant of integration.)

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

1.4 Step 3

Question Sequence

Question 1.3

Substitute into to determine the given integral in terms of x.

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