Pure 1 course · All short practice · Notes & examples

Maths4U Original · 9709 Pure 1

Signed integrals and geometric areas

Check a short answer, use a hint, then study the reasoning. These checks assess the final answer; use the exam-style problems to practise written explanations.

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Recall · M4U-P1-QP-INTEGRATION-AREAS-01

area under curve

Maths4U Original · Short practice

Find the area under \(y=3x^2\) above the x-axis from \(x=0\) to \(x=2\).

Enter one number or fraction. Round decimals to at least six decimal places when needed.

Method · M4U-P1-QP-INTEGRATION-AREAS-02

signed versus geometric

Maths4U Original · Short practice

Find the total geometric area between \(y=x\) and the x-axis from \(x=-1\) to \(x=1\).

Enter one number or fraction. Round decimals to at least six decimal places when needed.

Apply · M4U-P1-QP-INTEGRATION-AREAS-03

two curves

Maths4U Original · Short practice

Find the area between \(y=2x\) and \(y=x^2\) from \(x=0\) to \(x=2\).

Enter one number or fraction. Round decimals to at least six decimal places when needed.

Check understanding · M4U-P1-QP-INTEGRATION-AREAS-04

line and curve

Maths4U Original · Short practice

Find the area between \(y=4\) and \(y=x^2\) for \(-2\le x\le2\).

Enter one number or fraction. Round decimals to at least six decimal places when needed.

Fresh review variant · M4U-P1-QP-VAR-INTEGRATION-AREAS-01

area under curve

Maths4U Original · Short practice

Find the area under y=2x above the x-axis from x=0 to x=3.

Enter one number or fraction. Round decimals to at least six decimal places when needed.

Fresh review variant · M4U-P1-QP-VAR-INTEGRATION-AREAS-02

signed versus geometric

Maths4U Original · Short practice

Find the total geometric area between y=x and the x-axis from x=-2 to x=2.

Enter one number or fraction. Round decimals to at least six decimal places when needed.

Fresh review variant · M4U-P1-QP-VAR-INTEGRATION-AREAS-03

two curves

Maths4U Original · Short practice

Find the area between \(y=3x\) and \(y=x^2\) from x=0 to x=3.

Enter one number or fraction. Round decimals to at least six decimal places when needed.

Fresh review variant · M4U-P1-QP-VAR-INTEGRATION-AREAS-04

line and curve

Maths4U Original · Short practice

Find the area between y=9 and \(y=x^2\) for \(-3\le x\le3\).

Enter one number or fraction. Round decimals to at least six decimal places when needed.