Applications of Integration

Apply integrals to area, accumulation, and basic net-change interpretations.

Focus points

✓Interpret definite integrals as signed area.

✓Set up area-between-curves questions carefully.

✓Use accumulation ideas in applied settings.

Orin

The Wise Owl

Guides study flow, revision planning, and calmer focus sessions.

Practice set

Question lineup

Mark each one done as you go — finish them all to claim your chips.

6 revision prompts

Question 1

Find the area under y = 2 x + 1 from x = 0 to x = 3 .

Question 2

Find the area enclosed by y = x^{2} and y = 2 x .

Question 3OpenStax Calculus Volume 1, Sec. 5.1 Approximating Areas

Use a midpoint Riemann sum with 4 subintervals to approximate the area under f (x) = x^{2} on [0, 2] .

Question 4

The velocity of a particle is v (t) = 3 t^{2} - 4 t . Find the displacement from t = 0 to t = 3 .

Question 5

Set up an integral for the area between y = \sin x and the x -axis on [0, π] .

Question 6

If R (x) = 5 x + 2 is a rate of flow, find the accumulated quantity over [1, 4] .