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

Answer Key - Grade 12 Math Worksheet - Building Confidence

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

1. 1.

   Ari uses horizontal strips for the region between x = 5y and x = y². What is its area?

   125/6
2. 2.

   Bo uses horizontal strips for the region between x = 7y and x = y². What is its area?

   343/6
3. 3.

   Esme uses horizontal strips for the region between x = 8y and x = y². What is its area?

   256/3
4. 4.

   Jun uses horizontal strips for the region between x = 9y and x = y². What is its area?

   243/2
5. 5.

   Kira finds the area between x = 1 − y² and the y-axis, using strips in y. What is it?

   4/3
6. 6.

   Luz finds the area between x = 36 − y² and the y-axis, using strips in y. What is it?

   288
7. 7.

   Pia sets up the area between x = y² and x = y + 2 with horizontal strips. Which integral gives it?

   • ∫ from −1 to 2 of (y + 2 − y²) dx
   • ∫ from −1 to 2 of (y + 2 − y²) dy
   • ∫ from −1 to 2 of (y² − y − 2) dy
   • ∫ from 1 to 4 of (y + 2 − y²) dy
8. 8.

   Ren sets up the area between x = y² and x = 2y + 3 with horizontal strips. Which integral gives it?

   • ∫ from −1 to 3 of (2y + 3 − y²) dx
   • ∫ from −1 to 3 of (2y + 3 − y²) dy
   • ∫ from 1 to 9 of (2y + 3 − y²) dy
   • ∫ from −1 to 3 of (y² − 2y − 3) dy
9. 9.

   Tala sets up the area between x = y² − 2y and x = y + 4 with horizontal strips. Which integral gives it?

   • ∫ from −1 to 4 of (4 + 3y − y²) dy
   • ∫ from −1 to 4 of (y² − 3y − 4) dy
   • ∫ from −1 to 4 of (4 + 3y − y²) dx
   • ∫ from 3 to 8 of (4 + 3y − y²) dy
10. 10.

    Zee sets up the area between x = y² + 1 and x = 2y + 4 with horizontal strips. Which integral gives it?

    • ∫ from −1 to 3 of (y² − 2y − 3) dy
    • ∫ from −1 to 3 of (2y + 3 − y²) dx
    • ∫ from −1 to 3 of (2y + 3 − y²) dy
    • ∫ from 2 to 10 of (2y + 3 − y²) dy