Understanding Areas Under Curves

What is the integral of f(x) = x^2 from 0 to 3?

• 6

• 9

• 12

• 15

Calculate the area under the curve f(x) = sin(x) from 0 to π.

• 1

• 4

• 3

• 2

Find the area between the curves y = x^3 and y = x from x = 0 to x = 1.

• 0.25

• 0.75

• 0.5

• 0.1

Evaluate the definite integral of f(x) = e^x from 1 to 2.

• e^2 - e

• e^2 + e

• e^2 + 1

• e^2 - 1

What is the area under the curve f(x) = 1/x from x = 1 to x = 2?

• 1

• ln(3)

• ln(1)

• ln(2)

Determine the area under the curve f(x) = x^4 from x = 0 to x = 2.

• 8.0

• 10.2

• 6.4

• 4.8

Calculate the integral of f(x) = 3x^2 - 4 from x = 1 to x = 3.

• 12

• 18

• 6

• 24

What is the area between the curves y = x^2 and y = x from x = 0 to x = 1?

• 0.1

• 0.1667

• 0.5

• 0.25

Evaluate the integral of f(x) = cos(x) from 0 to π/2.

• 1

• 0

• 2

• π/4

Find the area under the curve f(x) = 2x + 1 from x = 0 to x = 4.

• 20

• 25

• 15

• 10