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 integration, or a random puzzle.

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2019

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2020