Grade 12 · Math · Calculus

12th grade The Fundamental Theorem of Calculus worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

When it’s done, scan the sheet with your phone and PencilGo marks it and picks the next one. Create a free account

Version

The Fundamental Theorem of Calculus

Grade 12 Math Worksheet - Building Confidence

NameDate

Circle the best answer, or write your answer on the line.

Esme uses F(x) = x³/3, an antiderivative of x². What is ∫ from 1 to 4 of x² dx?
Jun uses F(x) = x³/3, an antiderivative of x². What is ∫ from 2 to 5 of x² dx?
Kira uses F(x) = x³/3, an antiderivative of x². What is ∫ from 3 to 5 of x² dx?
Luz uses F(x) = x³/3, an antiderivative of x². What is ∫ from 2 to 4 of x² dx?
Noah defines g(x) = ∫ from 2 to x of (t² + 5) dt. What is g′(3)?
Ren defines g(x) = ∫ from 3 to x of (t² + 1) dt. What is g′(6)?
Zee defines g(x) = ∫ from 1 to x of (t² + 10) dt. What is g′(3)?
8.
Tala needs an antiderivative of f(x) = 3x² + 4 for Part 2. Which F(x) works?
- F(x) = 3x³ + 4x
- F(x) = x³ + 4
- F(x) = x³ + 4x
9.
Bo needs an antiderivative of f(x) = 2x + 5 for Part 2. Which F(x) works?
- F(x) = x² + 5x
- F(x) = 2x² + 5x
- F(x) = x² + 5
10.
Ari needs an antiderivative of f(x) = 5x⁴ + 3 for Part 2. Which F(x) works?
- F(x) = x⁵ + 3x
- F(x) = 5x⁵ + 3x
- F(x) = x⁵ + 3

The Fundamental Theorem of Calculus, both parts. Every version has 10 questions, and the answer key prints on the second page.

I can find g′(x) for g(x) = ∫ from a to x of f(t) dt, including x² and x at the bottom.
I can evaluate a definite integral as F(b) − F(a).
I can say where an accumulation is largest or smallest from the sign of f.
I can find an amount from its start and the integral of its rate.

Standard: none (beyond CCSS)

accumulation function: g(x) = ∫ from a to x of f(t) dt: the area so far.

antiderivative: A function F with F′ = f.

moving end: The end of the integral that is x, not a number.

Subtracted f(b) − f(a) using the function itself. Part 2 needs an antiderivative F with F′ = f.

Added F(b) and F(a). The theorem takes the top minus the bottom.

Took the derivative of f. The derivative of the accumulation is f itself.

What is the most common mistake with the fundamental theorem of calculus?

Subtracted f(b) − f(a) using the function itself. Part 2 needs an antiderivative F with F′ = f.

Are these 12th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

Every sheet you scan goes into your child’s record: dated, marked and ready for the year-end portfolio. Homeschool records