9231 FP2 · 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
Evaluate the following independent definite integrals on [0,1]. Show a suitable method.
Evaluate \(\int_0^1 x/(x^2+121)\,dx\).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Fresh review variant
Maths4U Original · Short practice
Evaluate the following independent definite integrals on [0,1]. Show a suitable method.
Evaluate \(\int_0^1 x/(x^2+144)\,dx\).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Method
Maths4U Original · Short practice
Evaluate the following independent definite integrals on [0,1]. Show a suitable method.
Evaluate \(\int_0^1 (x^2+144)^{-1/2}\,dx\).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Fresh review variant
Maths4U Original · Short practice
Evaluate the following independent definite integrals on [0,1]. Show a suitable method.
Evaluate \(\int_0^1 (x^2+169)^{-1/2}\,dx\).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Apply
Maths4U Original · Short practice
On \(0\le x\le 3\), the curve is \(y=\frac23(x+12)^{3/2}\).
Find V/π for the solid formed from the region under the curve.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Fresh review variant
Maths4U Original · Short practice
On \(0\le x\le 1\), the curve is \(y=\frac23(x+13)^{3/2}\).
Find V/π for the solid formed from the region under the curve.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Check understanding
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 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
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 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.