Integrate the function 1/((x-2)^(1/2)) from 1 to 3

 Exercise

$\int_1^3\frac{1}{\sqrt{x-2}}dx$

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Since the integral $\int_{1}^{3}\frac{1}{\sqrt{x-2}}dx$ has a discontinuity inside the interval, we have to split it in two integrals

$\int_{1}^{2}\frac{1}{\sqrt{x-2}}dx+\int_{2}^{3}\frac{1}{\sqrt{x-2}}dx$

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The integral $\int_{1}^{2}\frac{1}{\sqrt{x-2}}dx$ results in: $-2\sqrt{-1}$

$-2\sqrt{-1}$

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The integral $\int_{2}^{3}\frac{1}{\sqrt{x-2}}dx$ results in: $2$

$2$

 

Gather the results of all integrals

$-2\sqrt{-1}+2$

 

Calculate the power $\sqrt{-1}$ using complex numbers

$-2i+2$

$-2i+2$

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