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** Step-by-step Solution **

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Since the integral $\int_{0}^{2} s\left(1-x\right)^{-\frac{1}{2}}dx$ has a discontinuity inside the interval, we have to split it in two integrals

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$\int_{0}^{1} s\left(1-x\right)^{-\frac{1}{2}}dx+\int_{1}^{2} s\left(1-x\right)^{-\frac{1}{2}}dx$

Learn how to solve integral calculus problems step by step online. Integrate the function s(1-x)^(-1/2) from 0 to 2. Since the integral \int_{0}^{2} s\left(1-x\right)^{-\frac{1}{2}}dx has a discontinuity inside the interval, we have to split it in two integrals. The integral \int_{0}^{1} s\left(1-x\right)^{-\frac{1}{2}}dx results in: 2s. The integral \int_{1}^{2} s\left(1-x\right)^{-\frac{1}{2}}dx results in: -2\sqrt{-1}s. Gather the results of all integrals.

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