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.

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

   8/3
3. 3.

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

   8
4. 4.

   Luz finds the total area between y = x² − 3x and the x-axis for 0 ≤ x ≤ 4. What is it?

   19/3
5. 5.

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

   29/6
6. 6.

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

   13
7. 7.

   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
8. 8.

   Ren finds the area between y = sin x and y = cos x for π/4 ≤ x ≤ 5π/4. What is it, to the nearest hundredth?

   2.83
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