12th grade Definite integrals and net area worksheet

Definite integrals and net area

Grade 12 Math Worksheet - Challenge Me

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

1. 1.

   Esme sees the limit as n → ∞ of the sum, for i = 1 to n, of (3 + 2i/n)² · (2/n). Which integral is it?

   • ∫ from 0 to 2 of x² dx
   • ∫ from 3 to 5 of x² dx
   • ∫ from 3 to 5 of 2x² dx
2. 2.

   Jun sees the limit as n → ∞ of the sum, for i = 1 to n, of √(1 + 4i/n) · (4/n). Which integral is it?

   • ∫ from 1 to 5 of 4√x dx
   • ∫ from 0 to 4 of √x dx
   • ∫ from 1 to 5 of √x dx
3. 3.

   Kira sees the limit as n → ∞ of the sum, for i = 1 to n, of (2 + 3i/n)³ · (3/n). Which integral is it?

   • ∫ from 2 to 5 of x³ dx
   • ∫ from 2 to 5 of 3x³ dx
   • ∫ from 0 to 3 of x³ dx
4. 4.

   Luz sees the limit as n → ∞ of the sum, for i = 1 to n, of e^(2 + 3i/n) · (3/n). Which integral is it?

   • ∫ from 0 to 3 of eˣ dx
   • ∫ from 2 to 5 of 3eˣ dx
   • ∫ from 2 to 5 of eˣ dx
5. 5.

   Noah's scooter rolls forward at 8 m/s for 3 seconds, then back at 5 m/s for 2 seconds. What is its net change in position, in meters?
6. 6.

   Ren's tablet charges at 2.5% per minute for 4 minutes, then uses 1.5% per minute for 6 minutes. What is the net change in charge, in %?
7. 7.

   Sand pours into Zee's bucket at 7 cups per minute for 6 minutes, then leaks out at 3 cups per minute for 10 minutes. What is the net change in cups?
8. 8.

   What is the total area between the graph of f(x) = 3 − x and the x-axis from x = 0 to x = 5, for Tala's sketch?
9. 9.

   What is the total area between the graph of f(x) = 5 − x and the x-axis from x = 0 to x = 6, for Bo's sketch?
10. 10.

    What is the total area between the graph of f(x) = 6 − x and the x-axis from x = 0 to x = 8, for Ari's sketch?