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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 $$n>0$$):
$$\int_0^{a_n} x^n dx = 1$$
If you enjoyed this puzzle, check out Sunday Afternoon Maths XXXI,
puzzles about integration, or a random puzzle.

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