Area between a curve and an axis, and between two curves

Answer Key - Grade 12 Math Worksheet - Challenge Me

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

1. 1.

   Ari finds the total area enclosed by y = x³ and y = 25x. What is it?

   625/2
2. 2.

   Bo finds the total area enclosed by y = x³ and y = 9x. What is it?

   81/2
3. 3.

   Esme finds the total area enclosed by y = x³ and y = x. What is it?

   1/2
4. 4.

   Jun finds the total area enclosed by y = x³ and y = 16x. What is it?

   128
5. 5.

   The area between y = x² and the line y = k (k > 0) is 32/3. Luz solves for k. What is k?

   4
6. 6.

   The area between y = x² and the line y = k (k > 0) is 288. Milo solves for k. What is k?

   36
7. 7.

   The area between y = x² and the line y = k (k > 0) is 500/3. Noah solves for k. What is k?

   25
8. 8.

   Pia sets up the total area between y = x³ − x and the x-axis, which cross at x = −1, 0 and 1. Which expression gives it?

   • ∫ from −1 to 1 of (x³ − x) dx
   • ∫ from −1 to 1 of (x − x³) dx
   • ∫ from −1 to 0 of (x³ − x) dx − ∫ from 0 to 1 of (x³ − x) dx
   • ∫ from −1 to 0 of (x³ − x) dx + ∫ from 0 to 1 of (x³ − x) dx
9. 9.

   Tala sets up the total area between y = x³ and y = 9x, which cross at x = −3, 0 and 3. Which expression gives it?

   • ∫ from −3 to 3 of (9x − x³) dx
   • ∫ from −3 to 0 of (x³ − 9x) dx + ∫ from 0 to 3 of (x³ − 9x) dx
   • ∫ from −3 to 0 of (x³ − 9x) dx − ∫ from 0 to 3 of (x³ − 9x) dx
   • ∫ from −3 to 3 of (x³ − 9x) dx
10. 10.

    Zee sets up the total area between y = x³ − x² − 2x and the x-axis, which cross at x = −1, 0 and 2. Which expression gives it?

    • ∫ from −1 to 2 of (x³ − x² − 2x) dx
    • ∫ from −1 to 2 of (2x + x² − x³) dx
    • ∫ from −1 to 0 of (x³ − x² − 2x) dx − ∫ from 0 to 2 of (x³ − x² − 2x) dx
    • ∫ from −1 to 0 of (x³ − x² − 2x) dx + ∫ from 0 to 2 of (x³ − x² − 2x) dx