Area when you integrate in y, or the curves cross more than twice

Answer Key - Grade 12 Math Worksheet - Challenge Me

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

1. 1.

   Ari finds the area between x = 7 − y² and x = y² − 1, with horizontal strips. What is it?

   64/3
2. 2.

   Bo finds the area between x = 14 − y² and x = y² − 4, with horizontal strips. What is it?

   72
3. 3.

   Esme finds the area between x = 30 − y² and x = y² − 2, with horizontal strips. What is it?

   512/3
4. 4.

   Jun finds the area between x = 4 − y² and x = y² + 2, with horizontal strips. What is it?

   8/3
5. 5.

   Kira finds the total area between y = sin x and y = cos x for 0 ≤ x ≤ 7π/4, splitting at every crossing. What is it, to the nearest hundredth?

   4.66
6. 6.

   Luz finds the total area between y = sin x and y = cos x for 0 ≤ x ≤ 5π/3, splitting at every crossing. What is it, to the nearest hundredth?

   4.29
7. 7.

   Milo finds the total area between y = sin x and y = sin(2x) for 0 ≤ x ≤ 4π/3, splitting at every crossing. What is it, to the nearest hundredth?

   3.75
8. 8.

   Noah finds the total area between y = cos x and y = cos(2x) for 0 ≤ x ≤ 3π/2, splitting at every crossing. What is it, to the nearest hundredth?

   4.2
9. 9.

   In x the region between x = y² − 9 and x = y − 3 needs two integrals. Pia uses one integral in y instead. Which is it?

   • ∫ from −5 to 0 of (y + 6 − y²) dy
   • ∫ from −2 to 3 of (y² − y − 6) dy
   • ∫ from −2 to 3 of (y + 6 − y²) dy
   • ∫ from −2 to 3 of (y − 3) dy
10. 10.

    In x the region between x = 2y² and x = y + 1 needs two integrals. Ren uses one integral in y instead. Which is it?

    • ∫ from −1/2 to 1 of (2y² − y − 1) dy
    • ∫ from 1/2 to 2 of (y + 1 − 2y²) dy
    • ∫ from −1/2 to 1 of (y + 1 − 2y²) dy
    • ∫ from −1/2 to 1 of (y + 1) dy