Question 1

What is the value of the definite integral $$\$$int_1$$^3 (x^2$ - 1) \, dx as $$represented by the shaded area under the curve in the provided graph?

Accepted Answer

$$\frac{20}{3}$$

Question 2

Which of the following best describes the shaded region in the graph?

Accepted Answer

The area between $$y = x^2$ - 1$$ and the x-axis from $$x = 1 to$$ $$x = 3$$

Question 3

If the shaded area in the graph represents the net area between $$y = x^2$ - 1$$ and the x-axis from $$x = 1 to$$ $$x = 3$$, which integral would you use to calculate it?

Accepted Answer

$$\$$int_1$$^3 (x^2$ - 1) \, dx$$

Question 4

What is the y-coordinate of the point where the curve $$y = x^2$ - 1$$ intersects the vertical line $$x = 3$$?

Accepted Answer

$$8$$

Question 5

Which of the following statements is true about the shaded area in the graph?

Accepted Answer

It is bounded below by the x-axis and above by $$y = x^2$ - 1$$ from $$x = 1 to$$ $$x = 3$$

Question 6

Calculate the area of the shaded region using definite integration. What is the correct setup?

Accepted Answer

$$\$$int_1$$^3 (x^2$ - 1) \, dx$$

Question 7

What is the value of $$y$$ when $$x = 0$$ for the function $$y = x^2$ - 1$$?

Accepted Answer

$$-1$$

Question 8

Which of the following points is NOT on the curve $$y = x^2$ - 1$$?

Accepted Answer

$$(2, 2)$$

Question 9

If you wanted to find the total area between $$y = x^2$ - 1$$ and the x-axis from $$x = 0 to$$ $$x = 3$$, which integral would you use?

Accepted Answer

$$\$$int_0$$^3 |x^2$ - 1| \, dx$$

Question 10

What is the significance of the shaded area in the context of definite integrals?

Accepted Answer

It represents the net area between the curve and the x-axis over the interval $$[1, 3]$$

Chapter 13 Calculus Review: Integration and Applications

Guida di studio - Domande di pratica

Study guide - Flashcard