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

Answer Key - Grade 12 Math Worksheet - Building Confidence

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

1. 1.

   Ari finds the area between y = 4 − x² and the x-axis. What is it?

   32/3
2. 2.

   Bo finds the area between y = 9 − x² and the x-axis. What is it?

   36
3. 3.

   Esme finds the area between y = 16 − x² and the x-axis. What is it?

   256/3
4. 4.

   Jun finds the area between y = 25 − x² and the x-axis. What is it?

   500/3
5. 5.

   Kira finds the area between y = 2x and y = x². What is it?

   4/3
6. 6.

   Milo finds the area between y = 4x and y = x². What is it?

   32/3
7. 7.

   Pia sets up the area between y = 4 − x² and y = x + 2. Which integral gives it?

   • ∫ from −2 to 1 of (4 − x²) dx
   • ∫ from −2 to 1 of (2 − x − x²) dx
   • ∫ from 0 to 1 of (2 − x − x²) dx
   • ∫ from −2 to 1 of (x² + x − 2) dx
8. 8.

   Ren sets up the area between y = 6 − x² and y = x. Which integral gives it?

   • ∫ from 0 to 2 of (6 − x − x²) dx
   • ∫ from −3 to 2 of (x² + x − 6) dx
   • ∫ from −3 to 2 of (6 − x − x²) dx
   • ∫ from −3 to 2 of (6 − x²) dx
9. 9.

   Tala sets up the area between y = x + 6 and y = x². Which integral gives it?

   • ∫ from −2 to 3 of (x + 6 − x²) dx
   • ∫ from −2 to 3 of (x² − x − 6) dx
   • ∫ from −2 to 3 of (x + 6) dx
   • ∫ from 0 to 3 of (x + 6 − x²) dx
10. 10.

    Zee sets up the area between y = 8 − x² and y = x². Which integral gives it?

    • ∫ from −2 to 2 of (2x² − 8) dx
    • ∫ from −2 to 2 of (8 − 2x²) dx
    • ∫ from −2 to 2 of (8 − x²) dx
    • ∫ from 0 to 2 of (8 − 2x²) dx