12th grade Area when you integrate in y, or the curves cross more than twice worksheet

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

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?
2. 2.

   Bo uses horizontal strips for the region between x = 7y and x = y². What is its area?
3. 3.

   Jun uses horizontal strips for the region between x = 9y and x = y². What is its area?
4. 4.

   Kira finds the area between x = 1 − y² and the y-axis, using strips in y. What is it?
5. 5.

   Luz finds the area between x = 36 − y² and the y-axis, using strips in y. What is it?
6. 6.

   Milo finds the area between x = 49 − y² and the y-axis, using strips in y. What is it?
7. 7.

   Noah finds the area between x = 64 − y² and the y-axis, using strips in y. What is it?
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) dy
   • ∫ from −1 to 3 of (y² − 2y − 3) dy
   • ∫ from −1 to 3 of (2y + 3 − y²) dx
   • ∫ from 1 to 9 of (2y + 3 − y²) dy
9. 9.

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

   • ∫ from 3 to 8 of (4 + 3y − y²) dy
   • ∫ from −1 to 4 of (4 + 3y − y²) dx
   • ∫ from −1 to 4 of (y² − 3y − 4) dy
   • ∫ from −1 to 4 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 (2y + 3 − y²) dx
    • ∫ from 2 to 10 of (2y + 3 − y²) dy
    • ∫ from −1 to 3 of (2y + 3 − y²) dy
    • ∫ from −1 to 3 of (y² − 2y − 3) dy