Area between a curve and an axis, and between two curves

Grade 12 Math Worksheet - Challenge Me

NameDate

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

Ari finds the total area enclosed by y = x³ and y = 25x. What is it?
Esme finds the total area enclosed by y = x³ and y = x. What is it?
Jun finds the total area enclosed by y = x³ and y = 16x. What is it?
The area between y = x² and the line y = k (k > 0) is 36. Kira solves for k. What is k?
The area between y = x² and the line y = k (k > 0) is 32/3. Luz solves for k. What is k?
The area between y = x² and the line y = k (k > 0) is 500/3. Noah solves for k. What is k?
7.
Pia sets up the total area between y = x³ − x and the x-axis, which cross at x = −1, 0 and 1. Which expression gives it?
- ∫ from −1 to 0 of (x³ − x) dx + ∫ from 0 to 1 of (x³ − x) dx
- ∫ from −1 to 1 of (x − x³) dx
- ∫ from −1 to 0 of (x³ − x) dx − ∫ from 0 to 1 of (x³ − x) dx
- ∫ from −1 to 1 of (x³ − x) dx
8.
Ren sets up the total area between y = x³ − 4x and the x-axis, which cross at x = −2, 0 and 2. Which expression gives it?
- ∫ from −2 to 0 of (x³ − 4x) dx + ∫ from 0 to 2 of (x³ − 4x) dx
- ∫ from −2 to 2 of (x³ − 4x) dx
- ∫ from −2 to 0 of (x³ − 4x) dx − ∫ from 0 to 2 of (x³ − 4x) dx
- ∫ from −2 to 2 of (4x − x³) dx
9.
Tala sets up the total area between y = x³ and y = 9x, which cross at x = −3, 0 and 3. Which expression gives it?
- ∫ from −3 to 3 of (9x − x³) dx
- ∫ from −3 to 0 of (x³ − 9x) dx − ∫ from 0 to 3 of (x³ − 9x) dx
- ∫ from −3 to 0 of (x³ − 9x) dx + ∫ from 0 to 3 of (x³ − 9x) dx
- ∫ from −3 to 3 of (x³ − 9x) dx
10.
Zee sets up the total area between y = x³ − x² − 2x and the x-axis, which cross at x = −1, 0 and 2. Which expression gives it?
- ∫ from −1 to 0 of (x³ − x² − 2x) dx − ∫ from 0 to 2 of (x³ − x² − 2x) dx
- ∫ from −1 to 2 of (x³ − x² − 2x) dx
- ∫ from −1 to 0 of (x³ − x² − 2x) dx + ∫ from 0 to 2 of (x³ − x² − 2x) dx
- ∫ from −1 to 2 of (2x + x² − x³) dx

Area between a curve and an axis, and between two curves

Answer Key - Grade 12 Math Worksheet - Challenge Me

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

Ari finds the total area enclosed by y = x³ and y = 25x. What is it?
625/2
Esme finds the total area enclosed by y = x³ and y = x. What is it?
1/2
Jun finds the total area enclosed by y = x³ and y = 16x. What is it?
128
The area between y = x² and the line y = k (k > 0) is 36. Kira solves for k. What is k?
9
The area between y = x² and the line y = k (k > 0) is 32/3. Luz solves for k. What is k?
4
The area between y = x² and the line y = k (k > 0) is 500/3. Noah solves for k. What is k?
25
7.
Pia sets up the total area between y = x³ − x and the x-axis, which cross at x = −1, 0 and 1. Which expression gives it?
- ∫ from −1 to 0 of (x³ − x) dx + ∫ from 0 to 1 of (x³ − x) dx
- ∫ from −1 to 1 of (x − x³) dx
- ∫ from −1 to 0 of (x³ − x) dx − ∫ from 0 to 1 of (x³ − x) dx
- ∫ from −1 to 1 of (x³ − x) dx
8.
Ren sets up the total area between y = x³ − 4x and the x-axis, which cross at x = −2, 0 and 2. Which expression gives it?
- ∫ from −2 to 0 of (x³ − 4x) dx + ∫ from 0 to 2 of (x³ − 4x) dx
- ∫ from −2 to 2 of (x³ − 4x) dx
- ∫ from −2 to 0 of (x³ − 4x) dx − ∫ from 0 to 2 of (x³ − 4x) dx
- ∫ from −2 to 2 of (4x − x³) dx
9.
Tala sets up the total area between y = x³ and y = 9x, which cross at x = −3, 0 and 3. Which expression gives it?
- ∫ from −3 to 3 of (9x − x³) dx
- ∫ from −3 to 0 of (x³ − 9x) dx − ∫ from 0 to 3 of (x³ − 9x) dx
- ∫ from −3 to 0 of (x³ − 9x) dx + ∫ from 0 to 3 of (x³ − 9x) dx
- ∫ from −3 to 3 of (x³ − 9x) dx
10.
Zee sets up the total area between y = x³ − x² − 2x and the x-axis, which cross at x = −1, 0 and 2. Which expression gives it?
- ∫ from −1 to 0 of (x³ − x² − 2x) dx − ∫ from 0 to 2 of (x³ − x² − 2x) dx
- ∫ from −1 to 2 of (x³ − x² − 2x) dx
- ∫ from −1 to 0 of (x³ − x² − 2x) dx + ∫ from 0 to 2 of (x³ − x² − 2x) dx
- ∫ from −1 to 2 of (2x + x² − x³) dx