The Fundamental Theorem of Calculus

Answer Key - Grade 12 Math Worksheet - Building Confidence

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

1. 1.

   Esme uses F(x) = x³/3, an antiderivative of x². What is ∫ from 1 to 4 of x² dx?

   21
2. 2.

   Jun uses F(x) = x³/3, an antiderivative of x². What is ∫ from 2 to 5 of x² dx?

   39
3. 3.

   Luz uses F(x) = x³/3, an antiderivative of x². What is ∫ from 2 to 4 of x² dx?

   56/3
4. 4.

   Milo defines g(x) = ∫ from 1 to x of (t² + 3) dt. What is g′(5)?

   28
5. 5.

   Noah defines g(x) = ∫ from 2 to x of (t² + 5) dt. What is g′(3)?

   14
6. 6.

   Zee defines g(x) = ∫ from 1 to x of (t² + 10) dt. What is g′(3)?

   19
7. 7.

   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
8. 8.

   Pia needs an antiderivative of f(x) = 4x³ − 2 for Part 2. Which F(x) works?

   • F(x) = x⁴ − 2
   • F(x) = x⁴ − 2x
   • F(x) = 4x⁴ − 2x
9. 9.

   Bo needs an antiderivative of f(x) = 2x + 5 for Part 2. Which F(x) works?

   • F(x) = x² + 5x
   • F(x) = x² + 5
   • F(x) = 2x² + 5x
10. 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