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Complete the square for each quadratic in Exercises 28–33. Then describe the trigonometric substitution that would be appropriate if you were solving an integral that involved that quadratic.

2x24x+1

Short Answer

Expert verified

The completing square of the given quadratic equation is 2x-22-1,and the appropriate trigonometric substitution is localid="1649054906339" 2x-2=secu.

Step by step solution

01

Step 1. Given Information.

The given quadratic is2x24x+1.

02

Step 2. Completing the square for the given quadratic.

The complete square of the given quadratic equation is as follows:

2x2-4x+1=2x2-4x+22+1-22=2x-22-1

03

Step 3. Describing the trigonometric substitution. 

After completing the square for the given quadratic equation it is in the form ofx2-a2.

So, for solving an integral that involved the quadratic then the trigonometric substitution can be used islocalid="1649054922648" x=asecu.

Here,x=2x-2,a=1.

Thus, the appropriate trigonometric substitution islocalid="1649055042383" 2x-2=secu.

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