Definite Integrals and Their Properties

What happens to the integral when you switch the limits of integration?

• The integral doubles.

• The integral remains unchanged.

• The integral becomes zero.

• The integral changes sign.

If the integral from a to a is calculated, what is the result?

• The integral is equal to b.

• The integral is undefined.

• The integral is zero.

• The integral is equal to a.

How can you calculate the total area from A to C if you have integrals from A to B and B to C?

• Multiply the integrals from A to B and B to C.

• Divide the integral from A to B by B to C.

• Add the integrals from A to B and B to C.

• Subtract the integral from B to C from A to B.

What is the area under the curve from -1 to 1 of H(x) if it is given as 7?

• 21

• 0

• 7

• 14

What is the relationship between derivatives and integrals?

• Integrals are the anti-derivatives of derivatives.

• They are unrelated.

• Derivatives are the anti-derivatives of integrals.

• They are both the same.

What is the anti-derivative of x^n?

• x^(n+1)/(n+1)

• x^(n-1)/(n-1)

• nx^(n-1)

• nx^(n+1)

How do you evaluate the integral of a product of functions?

• Change the product to a single power and integrate.

• Separate the functions and integrate individually.

• Use the quotient rule.

• Use the product rule.

What is the result of evaluating the integral from 1 to 4 of x^(5/2)?

• 254/7

• 128

• 64

• 32

Which button do you press on a calculator to start evaluating a definite integral?

• Graph

• Math

• Mode

• Stat

What should you input into the calculator to evaluate an integral?

• Only the limits

• The function and limits, but not the variable

• The function, variable, and limits

• Only the function