mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

Integrals

$$\int_0^1 1 dx = 1$$
Find \(a_1\) such that:
$$\int_0^{a_1} x dx = 1$$
Find \(a_2\) such that:
$$\int_0^{a_2} x^2 dx = 1$$
Find \(a_n\) such that (for \(n>0\)):
$$\int_0^{a_n} x^n dx = 1$$

Show answer & extension

If you enjoyed this puzzle, check out Sunday Afternoon Maths XXXI,
puzzles about calculus, or a random puzzle.

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2025

Advent calendar 2024

Advent calendar 2023

Advent calendar 2022


List of all puzzles

Tags

multiplication angles albgebra shape digital clocks perfect numbers menace sequences decahedra cryptic crossnumbers perimeter factors probability symmetry functions money games sets indices cryptic clues means unit fractions sum to infinity integers products remainders logic powers speed multiplaction squares fractions consecutive integers quadratics cards averages integration chocolate tangents palindromes triangle numbers clocks geometry irreducible numbers median mean even numbers regular shapes taxicab geometry chalkdust crossnumber spheres dates coordinates ellipses complex numbers elections dice pentagons grids chess rectangles multiples trigonometry consecutive numbers axes bases time circles planes probabilty matrices medians parabolas 2d shapes ave folding tube maps square roots odd numbers crossnumbers prime numbers geometric means sums rugby pascal's triangle addition colouring dodecagons doubling factorials the only crossnumber wordplay arrows percentages people maths algebra calculus cubics determinants balancing books routes floors scales area geometric mean numbers volume crosswords polygons neighbours tournaments christmas coins xor sport prime factors quadrilaterals squares dominos star numbers triangles shapes surds graphs binary differentiation square numbers gerrymandering tiling lists division cube numbers number hexagons proportion digits range combinatorics polynomials digital products partitions advent square grids lines expansions 3d shapes

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2026