Reduction formulae: check 1
Difficulty: ★★☆Info
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.
Reduction formulae: review variant 1
Difficulty: ★★☆Info
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.
Reduction formulae: check 2
Difficulty: ★★☆Info
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.
Reduction formulae: review variant 2
Difficulty: ★★☆Info
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.
Reduction formulae: check 3
Difficulty: ★★☆Info
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.
Reduction formulae: review variant 3
Difficulty: ★★☆Info
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.
Reduction formulae: check 4
Difficulty: ★★☆Info
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.
Reduction formulae: review variant 4
Difficulty: ★★☆Info
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.