AIgo Notes

Home›Public Notes›Note details›Quiz

Quiz for:

Applications of Integration Formula Review - Antiderivatives, Definite Integrals, FTC, Area, Disk Me

Question 16

How does the disk method change if the axis of rotation is the y-axis?

A.The radius is the function itself

B.The radius is the distance from the y-axis to the curve

C.The radius is the function squared

D.The radius is the distance from the x-axis to the curve

Question 1

What is the symbol that represents the integral sign?

A.Sigma

B.Pi

C.Integral

D.Delta

Question 2

What is the result of the indefinite integral of a function?

A.A number

B.A function

C.A constant

D.An equation

Question 3

How do you evaluate a definite integral?

A.F of B - F of a

B.F of a - F of B

C.F of X

D.F of a

Question 4

What is the result of switching the limits of integration in a definite integral?

A.The same value

B.The negative of the original value

C.Zero

D.The square of the original value

Question 5

What is the formula for the definite integral from a to a of a function?

A.F of a - F of a

B.F of B - F of a

C.Zero

D.F of a

Question 6

What is the property of definite integrals that allows them to be split into multiple integrals?

A.Additivity

B.Subtractivity

C.Multiplicativity

D.Divisibility

Question 7

How can the area under a curve be calculated?

A.By evaluating the definite integral

B.By using the limit process

C.By summing the areas of rectangles

D.All of the above

Question 8

What is the formula for the sum of the first n natural numbers squared?

A.n * (n + 1) / 2

B.n^2 / 2

C.n * (n + 1) * (2n + 1) / 6

D.n^3 / 3

Question 9

What is the first term in the trapezoidal rule formula for approximating the area under a curve?

A.f(x0)

B.2 * f(x1)

C.f(x1)

D.f(xn)

Question 10

How does the coefficient pattern differ between the trapezoidal rule and Simpson's rule for approximating the area under a curve?

A.Trapezoidal rule has all coefficients as 1

B.Simpson's rule has alternating coefficients of 2 and 4

C.Both have alternating coefficients

D.Both have all coefficients as 1

Question 11

What is the fundamental theorem of calculus part 1 stating about the derivative of an integral?

A.The derivative of an integral is the integrand

B.The integral of a derivative is the function

C.The derivative of an integral is the area under the curve

D.The integral of a derivative is zero

Question 12

What does the net change theorem relate to?

A.The rate of change of a function

B.The accumulation of a rate function

C.The difference between two integrals

D.The average rate of change

Question 13

How is the area between two curves calculated?

A.By subtracting the integral of the bottom function from the integral of the top function

B.By adding the integrals of both functions

C.By integrating the difference of the functions

D.By integrating the sum of the functions

Question 14

What is the disk method used for?

A.Finding the area under a curve

B.Calculating the volume of a solid of revolution

C.Determining the length of a curve

D.Calculating the surface area of a solid

Question 15

What is the formula for the volume of a solid of revolution using the disk method about the x-axis?

A.Pi * integral from A to B of the radius squared dx

B.Pi * integral from A to B of the function squared dx

C.Pi * integral from A to B of the function dy

D.Pi * integral from A to B of the radius squared dy