Area when you integrate in y, or the curves cross more than twice
Grade 12 Math Worksheet - Challenge Me
Circle the best answer, or write your answer on the line.
Ari finds the area between x = 7 − y² and x = y² − 1, with horizontal strips. What is it?
Jun finds the area between x = 4 − y² and x = y² + 2, with horizontal strips. What is it?
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?
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?
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?
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?
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 −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
- ∫ from −5 to 0 of (y + 6 − y²) dy
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 (y + 1) dy
- ∫ from −1/2 to 1 of (2y² − y − 1) dy
- ∫ from −1/2 to 1 of (y + 1 − 2y²) dy
- ∫ from 1/2 to 2 of (y + 1 − 2y²) dy
In x the region between x = y² + 2y and x = y + 6 needs two integrals. Tala uses one integral in y instead. Which is it?
- ∫ from −3 to 2 of (y² + y − 6) dy
- ∫ from −3 to 2 of (6 − y − y²) dy
- ∫ from 3 to 8 of (6 − y − y²) dy
- ∫ from −3 to 2 of (y + 6) dy
In x the region between x = y + 1 and x = 3 − y² needs two integrals. Zee uses one integral in y instead. Which is it?
- ∫ from −2 to 1 of (2 − y − y²) dy
- ∫ from −1 to 2 of (2 − y − y²) dy
- ∫ from −2 to 1 of (y² + y − 2) dy
- ∫ from −2 to 1 of (3 − y²) dy