TMUA Official 2023 Paper 2 · Question 17

Official papers

Official 2023 Paper 2 · Q17

Paper 2CalculusNumber & counting

The ceiling of $x$ , written $\lceil x\rceil$ , is defined to be the value of $x$ rounded up to the nearest integer.

For example: $\lceil\pi\rceil=4$ , $\lceil2.1\rceil=3$ , $\lceil8\rceil=8$ .

What is the value of the following integral?

\int_0^{99}2^{\lceil x\rceil}\dd x.

2^{99}

2^{99}-1

2^{99}-2

2^{100}

2^{100}-1

2^{100}-2

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