What is the connection between the notation for a definite integral and a indefinite integral?

Definite is same as indefinite integral with an “a” and “b”

Turning summation notation into Integral:as the number of rectangles rise/approach Infinity....

The width of each rectangle decreases

Who discovered calculus?

Isaac Newton and Gottfried Leibniz

which of the following is a definition of a derivative?

Ratio of rate of change of function

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Questions 20

Answers

1
What is the constant rule?
(d/d) [c • u] = c • (du/dx)
(d/dx) [o] = 0
(d/d) [x^n] = n • x^(n-1)
(d/dx) [c] = 0
2
What is the connection between the notation for a definite integral and a indefinite integral?
Definite is the opposite as indefinite with d
Definite is same as indefinite integral with an “a” and “b”
Definite is the opposite as indefinite with c
Indefinite is same as definite integral with an “a” and “b”
3
If f’(x) = 3x², what is f(x)?
f(x) = x2 + c
f(x) = x3 + c
f’(x) = x3 + c
f(x) = x4 + c
4
Turning summation notation into Integral:as the number of rectangles rise/approach Infinity....
The width and length of each rectangle increases
The width of each rectangle decreases
The width of each rectangle increases
The width and length of each rectangle decreases
5
Evaluate the indefinite integral of ∫6 dx.
C
18+C
0
62/2
6
What is the Power Rule?
(d/dx) [u • v] = 100
(d/dx) [u • v] = u • (dv/dx) + v • (du/dx)
(d/dx) [c] = 0
(d/dx) [x^n] = n • x^(n - 1)
7
What symbol represents Integrals?
Ę
∫
Ï
(dy/dx)
8
Which of the following is NOT a rule for derivatives?
Power Rule
Constant Rule
Sum/Difference Rule
Zero Rule
9
∫ 24t³ dx = ?
6t4 + c
24 + c
C
6t4 + c
10
what is the second part of the fundamental theorem of calculus?
∫ab f(x) dx = F(b) - F(a)
(d/dx)∫ax f(t) dt = f(x)
11
∫4 dx = 4x+C is an example of what?
fundamental Theorem of calculus
Derivative
Expression
Integration
12
Who discovered calculus?
Archimedes and Euclid
Plato and Pythagoras
Euler and Fibonacci
Isaac Newton and Gottfried Leibniz
13
if f(x)=6x²+10
12
12x
6
6x
14
What is the purpose of the Sigma?
To show the difference between two number
To show the sum of a function
To show the product of a function
To make the equation look nice
15
Indefinite Integrals can also be known as
Anti Integral
Backwards Integral
Backwards Derivative
Antiderivatives
16
Which of the following is NOT a real world application for derivatives?
Ecology
Chemistry
Physics
Biology
17
If f’(x) = 10, what is f(x)?
f’(x) = 1x + c
f’(x) = 0x + c
f’(x) = 12x + c
f(x) = 10x + c
18
which of the following is a definition of a derivative?
Area under curve of a graph
The sigma of a function
The slope of a graph and function
Ratio of rate of change of function
19
Evaluate the definite integral ∫₀⁴-5 dx?
∫04 -5 dx = -20 units2
∫04 -5 dx = -20 units
∫04 -5 dx = 20 units2
∫04 -5 dx = 0 units2
20
Every integral has a C constant due to what rule for derivatives?
The Constant Rule
The Power Rule
The Sum/Difference Rule
The Constant Multiple Rule

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