Integrating Exponents and Rational Expressions

The video tutorial explains how to find the integral of 1 over the square root of x. It begins by rewriting the square root of x as a rational exponent, then applies the power rule for integration. The tutorial walks through the steps of changing the exponent's sign, integrating using the power rule, and simplifying the result to arrive at the final answer: 2 times the square root of x plus a constant of integration.

What is the first step in finding the integral of 1 over the square root of x?

• Move the variable to the numerator

• Simplify the expression

• Apply the power rule

• Rewrite the expression as a rational exponent

How can the square root of x be expressed as a rational exponent?

• x^2

• x^(1/2)

• x^(-1/2)

• x^(2/3)

Tags

CCSS.HSA.APR.A.1

What happens to the exponent when the x variable is moved to the numerator?

• It changes sign

• It becomes positive

• It doubles

• It remains the same

Which rule is used to integrate x raised to a power?

• Chain rule

• Power rule

• Product rule

• Quotient rule

What is the result of adding 1 to the exponent -1/2?

• 3/2

• -1

• 0

• 1/2

How do you eliminate the fraction in the expression x^(1/2) / (1/2)?

• Add 2

• Divide by 2

• Multiply by 2

• Subtract 2

Tags

CCSS.7.EE.A.1

What is the final form of the integral of 1 over the square root of x?

• 2x^(-1/2) + C

• x^(-1/2) + C

• 2x^(1/2) + C

• x^(1/2) + C

What is the equivalent expression for x^(1/2)?

• x^2

• 1/x

• Square root of x

• Cube root of x

What constant is added to the integral result?

• A

• B

• C

• D