Calculus

AdvancedMaths revision

Applications of Integration

Use integration for area, volume, average value and accumulated change.

Open calculator

Focus points

✓Set up area between curves.

✓Compute volumes of revolution.

✓Interpret accumulated rates.

orin

Orin

The Wise Owl

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

Practice set

Question lineup

Try each question first, reveal a hint when you need one, then check the worked answer. Mark them done as you go — finish the set to claim your chips.

10 revision questions

Question 1FluencyCore

Original practice · Free Online Revision

Skill · area between curves

Find the area between y=x and y=x² on 0≤x≤1.

Question 2FluencyCore

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Skill · enclosed area

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

Question 3FluencyCore

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Skill · volume of revolution

Find the volume formed by rotating y=x, 0≤x≤2, about the x-axis.

Question 4FluencyCore

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Skill · volume of revolution

Find the volume rotating the region under y=√x from x=0 to 4 about x-axis.

Question 5FluencyCore

Original practice · Free Online Revision

Skill · average value

Find average value of f(x)=x² on [0,3].

Question 6ApplicationCore

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Skill · accumulation

A velocity is v(t)=3t²−12t+9 for 0≤t≤4. Find displacement over the interval.

Question 7ChallengeStretch

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Skill · total distance

For the same velocity, find total distance travelled on 0≤t≤4.

Question 8ApplicationStretch

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Skill · area between curves

Find the area enclosed by y=x² and y=2x+3.

Question 9ApplicationCore

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Skill · accumulated rate

A tank inflow rate is r(t)=10+2t L/min for 0≤t≤5. If it begins with 40 L, how much water after 5 min?

Question 10ReasoningCore

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Skill · setup reasoning

Why must area between curves usually be split when the curves cross inside the interval?