Exploring Anti-Derivatives in Calculus

What is the main goal of finding an antiderivative?

• To calculate the area under a curve.

• To solve differential equations.

• To find the original function from its derivative.

• To determine the slope of a function.

If the derivative of a function is 2x, what is the original function?

• 2x^2

• x^2

• 2x

• x^3

Why do we add a constant term (C) when finding an antiderivative?

• To simplify the derivative.

• To ensure the function is continuous.

• To make the equation more complex.

• To account for any possible constant in the original function.

What is the antiderivative of 3x^2?

• x^2

• 3x

• 3x^3

• x^3

In the example 3x^2 - x + 1, what is the coefficient of x^2 in the original function?

• 3

• -1

• -1/2

• 1

What is the antiderivative of 1?

• x

• 1

• 0

• x^2

Given the derivative -1/x^2 and a point (2,1), what is the constant term (C) in the original function?

• 0

• 1/2

• 1

• 2

What is the antiderivative of -1/x^2?

• x

• -1/x

• 1/x

• -x

Why is it important to know the point (2,1) in the example with -1/x^2?

• To solve for x.

• To find the specific value of the constant term.

• To determine the slope at that point.

• To calculate the area under the curve.

What will be the focus of the next chapter after a brief hiatus from antiderivatives?

• Integration techniques

• Advanced antiderivatives

• Applications of derivatives

• Differential equations