Area when you integrate in y, or the curves cross more than twice
Grade 12 Math Worksheet
Circle the best answer, or write your answer on the line.
Ari finds the area of the region bounded by x = y², the line x = y + 2 and the x-axis, with y ≥ 0. What is it?
Bo finds the area of the region bounded by x = y², the line x = y + 6 and the x-axis, with y ≥ 0. What is it?
Esme finds the area of the region bounded by x = y², the line x = y + 12 and the x-axis, with y ≥ 0. What is it?
Jun finds the area of the region bounded by x = y², the line x = y + 20 and the x-axis, with y ≥ 0. What is it?
Kira finds the total area between y = x³ and y = x² + 2x, which cross at x = −1, 0, 2. What is it, to the nearest hundredth?
Luz finds the total area between y = x³ and y = x² + 6x, which cross at x = −2, 0, 3. What is it, to the nearest hundredth?
Milo finds the total area between y = x³ + x² and y = 2x, which cross at x = −2, 0, 1. What is it, to the nearest hundredth?
Noah finds the total area between y = x³ and y = 5x² − 6x, which cross at x = 0, 2, 3. What is it, to the nearest hundredth?
Ren rewrites the region bounded by y = √x, y = 0 and x = 4 with horizontal strips. Which integral gives its area?
- ∫ from 0 to 4 of (4 − y²) dy
- ∫ from 0 to 2 of (y²) dy
- ∫ from 0 to 2 of (4 − y²) dy
- ∫ from 0 to 2 of (y² − 4) dy
Zee rewrites the region bounded by y = ln x, y = 0 and x = e² with horizontal strips. Which integral gives its area?
- ∫ from 0 to 2 of (e² − eʸ) dy
- ∫ from 0 to 2 of (eʸ − e²) dy
- ∫ from 0 to 2 of (eʸ) dy
- ∫ from 0 to e² of (e² − eʸ) dy