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 integration, 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

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

Archive

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