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

Answer Key - Grade 12 Math Worksheet

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

1. 1.

   Ari finds the area between y = 5 − x² and y = x² − 3. What is it?

   64/3
2. 2.

   Bo finds the area between y = 10 − x² and y = x² − 8. What is it?

   72
3. 3.

   Esme finds the area between y = 3 − x² and y = x² + 1. What is it?

   8/3
4. 4.

   Jun finds the area between y = 20 − x² and y = x² − 12. What is it?

   512/3
5. 5.

   Kira finds the total area between y = x² − 2x and the x-axis for 0 ≤ x ≤ 4. What is it?

   8
6. 6.

   Milo finds the total area between y = x² − 1x and the x-axis for 0 ≤ x ≤ 3. What is it?

   29/6
7. 7.

   Noah finds the total area between y = x² − 4x and the x-axis for 0 ≤ x ≤ 5. What is it?

   13
8. 8.

   Pia finds the area between y = sin x and y = cos x for 0 ≤ x ≤ π/4. What is it, to the nearest hundredth?

   0.41
9. 9.

   Tala finds the area between y = 1 and y = cos x for 0 ≤ x ≤ π/2. What is it, to the nearest hundredth?

   0.57
10. 10.

    Zee finds the area between y = 2 and y = 1 + sin x for 0 ≤ x ≤ π. What is it, to the nearest hundredth?

    1.14