9709 P3 · Notes & worked examples
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
Maths4U Original · Short practice
The integrand is \(\displaystyle f(x)=\frac{3}{3 x + 2}\), on \(\displaystyle x>- \frac{2}{3}\).
Find K in the primitive K ln(3x+2)+C on the stated domain.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Fresh review variant
Maths4U Original · Short practice
The integrand is \(\displaystyle f(x)=\frac{4}{x + 3}\), on \(x>-3\).
Find K in the primitive K ln(1x+3)+C on the stated domain.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Method
Maths4U Original · Short practice
The integrand is \(\displaystyle f(x)=\frac{4}{x + 3}\), on \(x>-3\).
Find f(0).
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Fresh review variant
Maths4U Original · Short practice
The integrand is \(\displaystyle f(x)=\frac{5}{2 x + 4}\), on \(x>-2\).
Find f(0).
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Apply
Maths4U Original · Short practice
The integrand is \(\displaystyle f(x)=\frac{10 x + 20}{x^{2} + 4 x + 17}\), on real x.
Find the definite integral from 0 to 1.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Fresh review variant
Maths4U Original · Short practice
The integrand is \(\displaystyle f(x)=\frac{4 x + 2}{x^{2} + x + 2}\), on real x.
Find the definite integral from 0 to 1.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Check understanding
Maths4U Original · Short practice
The integrand is \(\displaystyle f(x)=\frac{4 x + 2}{x^{2} + x + 2}\), on real x.
Find the minimum value of the denominator.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Fresh review variant
Maths4U Original · Short practice
The integrand is \(\displaystyle f(x)=\frac{6 x + 6}{x^{2} + 2 x + 5}\), on real x.
Find the minimum value of the denominator.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.