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 2023

Advent calendar 2022

Advent calendar 2021

Advent calendar 2020


List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2024