The Fundamental Theorem of Calculus

Answer Key - Grade 12 Math Worksheet

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

1. 1.

   Esme evaluates ∫ from 1 to 2 of (3x² + 2x) dx with an antiderivative. What is it?

   10
2. 2.

   Kira evaluates ∫ from 3 to 4 of (3x² + 2x) dx with an antiderivative. What is it?

   44
3. 3.

   Luz evaluates ∫ from 1 to 5 of (3x² + 2x) dx with an antiderivative. What is it?

   148
4. 4.

   Milo defines g(x) = ∫ from 1 to x² of (t + 3) dt. What is g′(2)?

   28
5. 5.

   Ren defines g(x) = ∫ from 1 to x² of (t + 5) dt. What is g′(2)?

   36
6. 6.

   Zee defines g(x) = ∫ from 1 to x² of (t + 6) dt. What is g′(4)?

   176
7. 7.

   Tala defines g(x) = ∫ from 0 to x of f(t) dt, with f shown. Where on [0, 7] does g have its largest value?

   • x = 1, where the graph of f is at its highest
   • x = 3, where f changes from + to −
   • x = 7, the right end
8. 8.

   Pia defines g(x) = ∫ from 0 to x of f(t) dt, with f shown. Where on [0, 9] does g have its smallest value?

   • x = 4, where f changes from − to +
   • x = 9, the right end
   • x = 2, where the graph of f is at its lowest
9. 9.

   Bo defines g(x) = ∫ from 0 to x of f(t) dt, with f shown. Where on [0, 6] does g have its largest value?

   • x = 2, where the graph of f is at its highest
   • x = 6, the right end
   • x = 5, where f changes from + to −
10. 10.

    Ari defines g(x) = ∫ from 0 to x of f(t) dt, with f shown. Where on [0, 8] does g have its smallest value?

    • x = 2, where f changes from − to +
    • x = 8, the right end
    • x = 1, where the graph of f is at its lowest