Essential Knowledge Check Calc BC 6.1-6.5

What is the relationship that this unit establishes between differentiation and integration according to the Fundamental Theorem of Calculus?

• Integration is the process of finding the original function from its derivative.

• Differentiation determines the accumulation of change over an interval as bounded by rate functions.

• Integration is simply differentiation in reverse order.

• Differentiation and integration are unrelated mathematical practices.

What does the area of the region between the graph of a rate of change function and the x-axis represent?

• The total distance traveled

• The accumulation of change

• The velocity of an object

• The derivative of the function

Tags

CCSS.HSF.IF.B.4

If the rate of change is positive over an interval, what is the nature of the accumulated change?

• Negative

• Zero

• Positive

• Undefined

Tags

CCSS.HSF-LE.A.1B

According to the learning material, how can accumulation of change be evaluated more easily in some cases?

• By using algebraic manipulation

• By using calculus

• By using geometry

• By using arithmetic operations

What is the unit for the area of a region defined by rate of change?

• The unit for the rate of change

• The unit for the independent variable

• The unit for the rate of change multiplied by the unit for the independent variable

• The unit for the dependent variable

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

What can definite integrals be approximated using?

• Algebraic expressions only

• Geometric and numerical methods

• Probability and statistics

• Differential equations

Which of the following is NOT a method mentioned for approximating definite integrals?

• Left Riemann sum

• Right Riemann sum

• Midpoint Riemann sum

• Integral exponentiation

What may be possible to determine when analyzing the behavior of a function in relation to definite integrals?

• The exact value of the definite integral

• Whether an approximation is an underestimate or overestimate for the value of the definite integral

• The derivative of the function at a specific point

• The total number of discontinuities in the function

What is the limiting case of the Riemann sum used to interpret?

• A differential equation

• A definite integral

• An indefinite integral

• A function's maximum value

What does a Riemann sum require?

• A partition of an interval [a, b] and the sum of squares

• A partition of an interval [a, b] and the sum of products

• A partition of an interval [a, b] and the sum of roots

• A partition of an interval [a, b] and the sum of differences