Calculus Area

Calculate the area between the curves y = x^2 and y = 2x from x = 0 to x = 2.

• 5/3

• 2/3

• 4/3

• 1/2

Find the area enclosed by the curves y = x^3 and y = x^2 from x = -1 to x = 1.

• 1/8

• 1/12

• 1/10

• 1/6

Determine the area between the curves y = sin(x) and y = cos(x) from x = 0 to x = π/2.

• 1

• The area is negative

• The area is zero

• The area is infinite

Calculate the area bounded by the curves y = e^x and y = ln(x) from x = 1 to x = 2.

• The area bounded by the curves y = e^x and y = ln(x) from x = 1 to x = 2 is exactly 0.

• The area bounded by the curves y = e^x and y = ln(x) from x = 1 to x = 2 is negative.

• The area bounded by the curves y = e^x and y = ln(x) from x = 1 to x = 2 is approximately 2.5.

• The area bounded by the curves y = e^x and y = ln(x) from x = 1 to x = 2 is approximately 1.718.

Find the area between the curves y = x^2 and y = 4x - x^2 from x = 0 to x = 2.

• The area between the curves y = x^2 and y = 4x - x^2 from x = 0 to x = 2 is 10 square units.

• The area between the curves y = x^2 and y = 4x - x^2 from x = 0 to x = 2 is 8/3 square units.

• The area between the curves y = x^2 and y = 4x - x^2 from x = 0 to x = 2 is 4 square units.

• The area between the curves y = x^2 and y = 4x - x^2 from x = 0 to x = 2 is 2 square units.

Determine the area enclosed by the curves y = √x and y = x^2 from x = 0 to x = 1.

• The area enclosed by the curves y = √x and y = x^2 from x = 0 to x = 1 is 1/3 square units.

• The area enclosed is 1/2 square units

• The area enclosed is 2/3 square units

• The area enclosed is 1 square unit

Calculate the area between the curves y = 2x and y = x^2 - 1 from x = -1 to x = 2.

• 9.73

• 14.25

• 7.89

• 11.33

Find the area bounded by the curves y = x^3 and y = x^4 from x = 0 to x = 1.

• 1/25

• 1/10

• 1/15

• 1/20

Determine the area between the curves y = 1/x and y = x^2 from x = 1 to x = 2.

• The area between the curves y = 1/x and y = x^2 from x = 1 to x = 2 is negative.

• The area between the curves y = 1/x and y = x^2 from x = 1 to x = 2 is approximately 0.3466 square units.

• The area between the curves y = 1/x and y = x^2 from x = 1 to x = 2 is exactly 0.5 square units.

• The area between the curves y = 1/x and y = x^2 from x = 1 to x = 2 is approximately 1.5 square units.

Calculate the area enclosed by the curves y = e^x and y = e^(2x) from x = 0 to x = 1.

• (1/4)e^2 - (1/4)e

• (1/5)e^2 - (1/5)e

• (1/2)e^2 - (1/2)e

• (1/3)e^2 - (1/3)e