TMUA 2023 Paper 2 Q17 — Worked Solution

P2·Integration, Sequences & Series·5.5Official · 2023 · Q17

ceiling-functionstep-integralgeometric-series

The ceiling of

x

, written

⌈ x ⌉

, is defined to be the value of

x

rounded up to the nearest integer.For example:

⌈ π ⌉ = 4

⌈ 2.1 ⌉ = 3

⌈ 8 ⌉ = 8

.What is the value of the following integral?

\int_{0}^{99} 2^{⌈ x ⌉} d x

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