Integration Using Completing the Square Quiz

What is the primary focus of using completing the square in integration?

• When the expression is a linear polynomial

• When the quadratic is in the numerator

• When the quadratic in the denominator is not factorable

• When the quadratic in the denominator is factorable

In the first example, what is the constant added to complete the square for the expression x^2 + 10x + 26?

• 15

• 20

• 25

• 30

What is the antiderivative formula used in the first example after completing the square?

• Exponential function

• Inverse tangent

• Natural logarithm

• Inverse sine

In the second example, what is the value of 'a' in the inverse tangent formula after completing the square?

• 1

• 2

• 3

• 4

What is the completed square form of x^2 - 4x + 8 in the second example?

• (x - 2)^2 + 4

• (x - 2)^2 + 8

• (x + 2)^2 + 4

• (x + 2)^2 + 8

In the third example, what is the antiderivative formula used after completing the square under a square root?

• Natural logarithm

• Exponential function

• Inverse sine

• Inverse tangent

What is the completed square form of x^2 + 6x in the third example?

• (x + 3)^2

• (x - 3)^2

• (x + 2)^2

• (x - 2)^2

In the final example, what substitution is initially attempted?

• U = x^2 + 8x + 17

• U = x^2 + 6x + 9

• U = x^2 - 4x + 8

• U = x^2 + 10x + 26

What is the purpose of multiplying the numerator by 2 in the final example?

• To factor the quadratic

• To complete the square

• To match the derivative of the substitution

• To simplify the expression

What is the final form of the expression after completing the square in the final example?

• (x - 3)^2 + 1

• (x + 4)^2 + 1

• (x + 3)^2 + 1

• (x - 4)^2 + 1