mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

Find them all

Find all continuous positive functions, \(f\) on \([0,1]\) such that:
$$\int_0^1 f(x) dx=1\\ \mathrm{and }\int_0^1 xf(x) dx=\alpha\\ \mathrm{and }\int_0^1 x^2f(x) dx=\alpha^2$$

Show answer & extension

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

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2020

Advent calendar 2019

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018


List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2021