Reduction formulae · 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

Reduction formulae — objective 1

Maths4U Original · Short practice

For integer \(\displaystyle n\ge 0\), define \(I_n=\int_0^1x^ne^{2x}\,dx\).

Find \(\displaystyle I_{0}\).

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

Fresh review variant

Reduction formulae — objective 1

Maths4U Original · Short practice

For integer \(\displaystyle n\ge 0\), define \(I_n=\int_0^1x^ne^{3x}\,dx\).

Find \(\displaystyle I_{0}\).

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

Method

Reduction formulae — objective 2

Maths4U Original · Short practice

For integer \(\displaystyle n\ge 0\), define \(I_n=\int_0^1x^ne^{3x}\,dx\).

Find \(\displaystyle I_{4}\).

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

Fresh review variant

Reduction formulae — objective 2

Maths4U Original · Short practice

For integer \(\displaystyle n\ge 0\), define \(I_n=\int_0^1x^ne^{1x}\,dx\).

Find \(\displaystyle I_{2}\).

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

Apply

Reduction formulae — objective 3

Maths4U Original · Short practice

For integer \(\displaystyle n\ge 0\), define \(I_n=\int_0^1x^ne^{1x}\,dx\).

Find \(\displaystyle I_{3}\).

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

Fresh review variant

Reduction formulae — objective 3

Maths4U Original · Short practice

For integer \(\displaystyle n\ge 0\), define \(I_n=\int_0^1x^ne^{2x}\,dx\).

Find \(\displaystyle I_{4}\).

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

Check understanding

Reduction formulae — objective 4

Maths4U Original · Short practice

For integer \(\displaystyle n\ge 0\), define \(I_n=\int_0^1x^ne^{2x}\,dx\).

Find the positive coefficient of \(\displaystyle I_{2}\) subtracted in the recurrence for \(\displaystyle I_{3}\).

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

Fresh review variant

Reduction formulae — objective 4

Maths4U Original · Short practice

For integer \(\displaystyle n\ge 0\), define \(I_n=\int_0^1x^ne^{3x}\,dx\).

Find the positive coefficient of \(\displaystyle I_{3}\) subtracted in the recurrence for \(\displaystyle I_{4}\).

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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