Understanding Indefinite Integrals

What is the first step in finding an anti-derivative of a function?

• Divide by the exponent

• Multiply by the exponent

• Add one to the exponent

• Subtract one from the exponent

Why is the constant of integration important when finding an anti-derivative?

• It accounts for all possible vertical shifts of the function

• It affects the domain of the function

• It determines the slope of the function

• It changes the degree of the polynomial

Which property allows you to factor out constants from an integral?

• Addition property

• Subtraction property

• Constant multiple property

• Quotient property

How can integrals be simplified under addition or subtraction?

• By breaking them into separate integrals

• By adding a constant

• By dividing the integrals

• By multiplying the integrals

What is the integral of cosine?

• Cosine

• Sine

• Negative cosine

• Negative sine

Which function's derivative is the negative cosine?

• Sine

• Negative sine

• Negative cosine

• Cosine

What is the integral of e^x?

• 1/x

• ln(x)

• x^e

• e^x

What is the integral of 1/x?

• e^x

• ln|x|

• x^2

• 1/x^2

What is the integral of b^x?

• ln(b^x)

• b^x / ln(b)

• x^b

• b^x

What must be added to the integral of 1/x to ensure it is correct?

• An exponent

• A constant

• A logarithm

• An absolute value