CPM Homework Help : CALC3RD Problem 6-174

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6-174.

Examine the integrals below. Consider the multiple tools available for evaluating integrals and use the best strategy for each part. Evaluate each integral and briefly describe your method.

$\int _ { 1 } ^ { 10 } 2 \sqrt { x - 1 } d x$
Hint (a):
Convert the radical to an exponent. Then use the form $u^{power}du$ .

$\int ( 3 x - 2 ) ^ { 2 } d x$
Method 1(b):
If $u = (3x − 2)$ , then you need to add a $du$ . In this case, it would be $3 dx$ .
Since you already have a $dx$ , add a $3$ taking out a $(1/3)$ to compensate.
Method 2(b):
Multiply $(3x − 2) (3x − 2)$ .
Then take the antiderivative.

$\int - \frac { 1 } { 1 + x ^ { 2 } } d x$
Hint (c):
Use the rule for one of the inverse trig functions.

$\int ( 6 t ^ { - 3 / 2 } + 7 t ^ { 1 / 4 } ) d t$
Hint (d):
This is a sum of power functions. Take the antiderivative.

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