Limits of areas · Short practice

Check a final answer, then explain the reasoning on paper. Guest progress stays in this browser; an account saves future checks without overwriting your first result.

Recall

Limits of areas and sums — objective 1

Maths4U Original · Short practice

Consider the area under \(y=x^2+13x\) on \(0\le x\le 2\). For the finite sums use 15 equal subintervals.

Find the exact integral.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Limits of areas and sums — objective 1

Maths4U Original · Short practice

Consider the area under \(y=x^2+14x\) on \(0\le x\le 3\). For the finite sums use 16 equal subintervals.

Find the exact integral.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Method

Limits of areas and sums — objective 2

Maths4U Original · Short practice

Consider the area under \(y=x^2+14x\) on \(0\le x\le 3\). For the finite sums use 16 equal subintervals.

Find the right-endpoint rectangle sum.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Limits of areas and sums — objective 2

Maths4U Original · Short practice

Consider the area under \(y=x^2+15x\) on \(0\le x\le 4\). For the finite sums use 17 equal subintervals.

Find the right-endpoint rectangle sum.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Apply

Limits of areas and sums — objective 3

Maths4U Original · Short practice

Consider the area under \(y=x^2+15x\) on \(0\le x\le 4\). For the finite sums use 17 equal subintervals.

Find the left-endpoint rectangle sum.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Limits of areas and sums — objective 3

Maths4U Original · Short practice

Consider the area under \(y=x^2+16x\) on \(0\le x\le 2\). For the finite sums use 18 equal subintervals.

Find the left-endpoint rectangle sum.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Check understanding

Limits of areas and sums — objective 4

Maths4U Original · Short practice

Consider the area under \(y=x^2+16x\) on \(0\le x\le 2\). For the finite sums use 18 equal subintervals.

Find the difference between right and left sums.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Limits of areas and sums — objective 4

Maths4U Original · Short practice

Consider the area under \(y=x^2+17x\) on \(0\le x\le 3\). For the finite sums use 19 equal subintervals.

Find the difference between right and left sums.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

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