# Antiderivatives And The Fundamental Theorem Of Calculus

10 Questions | Total Attempts: 119  Settings  This theory can be summed up as the theorem that links the concept of differentiating a function with the concept of integrating a function. In other words, the theorem shows that these 2 operations are fundamentally inverses of one another. Take our quiz to practice your knowledge about calculus and see how well you are doing.

• 1.
What does the theorem imply?
• A.

That the changes in a quantity over time adds up to the net change in quantity

• B.

That the sum of infinitesimal changes in a quantity over time adds up to the net change in quantity

• C.

That the addition in quantity over a small period of time adds up to the net change in quantity

• D.

That a given function f(x) adds up to the net change in quantity

• 2.
What does "summing up" correspond to?
• A.

Fusion

• B.

Integration

• C.

Logarithm

• D.

Cumulus

• 3.
From what is the velocity function derived from?
• A.

The position function

• B.

The logarithm function

• C.

Optics

• D.

Cosinus

• 4.
How can you sum up the theorem using a formula?
• A.

Dx=dt

• B.

Dx=v(t)dt

• C.

Dt=v(x)dx

• D.

Dt=vx

• 5.
How many parts of the theorem are there?
• A.

2

• B.

3

• C.

4

• D.

5

• 6.
What does the first part of the theorem deal with?
• A.

Anti derivatives

• B.

The derivative of an anti derivative

• C.

Function f(x)

• D.

Function lnx

• 7.
What does the second part of the theorem deal with?
• A.

Definite integrals

• B.

The relationship between anti derivatives and definite integrals

• C.

Anti derivatives

• D.

Function f(x)

• 8.
What does the corollary assume?
• A.

The continuity on the whole interval

• B.

The continuity on the function

• C.

The continuity on the window of solutions

• D.

The limits of the whole interval

• 9.
What is the second part of the theorem called?
• A.

The Newton-Leibniz axiom

• B.

The Pythagoras axiom

• C.

The Newton-Leibniz function

• D.

The Newton-Leibniz theorem

• 10.
What is the mean value theorem?
• A.

It states that for a given planar arc between 2 endpoints, there is at least 1 point at which the tangent to the arc is parallel to the secant through its axe

• B.

It states that for a given set of endpoints, there is at least 1 point at which the tangent to the arc is parallel to the secant through its endpoints

• C.

It states that for a given planar arc between 2 endpoints, there is at least 1 point at which the tangent to the arc is parallel to the secant through its endpoints

• D.

It states that for a given planar arc between 2 endpoints, there are at least 3 points at which the tangent to the arc is parallel to the secant through its endpoints Back to top