Definite integrals: area and volume of revolution

Question 1 of 10

∫ₐᵃ f(x) dx =

Question 2 of 10

The curve y = 3x² meets the line y = 12 at x = 2. Find the area enclosed by the curve, the y-axis and the line y = 12.

Question 3 of 10

Find the area under the line y = 5 from x = 2 to x = 5.

Question 4 of 10

The area under the curve y = f(x) from x = a to x = b is

Question 5 of 10

The volume formed when y = f(x) is rotated about the x-axis from a to b is

Question 6 of 10

Evaluate ∫ from 1 to 3 of x⁴ dx.

Question 7 of 10

Find the area bounded by y = 4x², the x-axis and the lines x = 1 and x = 3.

Question 8 of 10

Find the area bounded by y = 6x², the x-axis and the lines x = 1 and x = 3.

Question 9 of 10

The area under a curve above the x-axis is positive.

Question 10 of 10

Find the area enclosed by the curve y = x² − 4 and the x-axis.