Integrate the function x^(-1/2) from -1 to 4

 Exercise

$\int_{-1}^4\left(x^{-\frac{1}{2}}\right)dx$

 

Since the integral $\int_{-1}^{4} x^{-\frac{1}{2}}dx$ has a discontinuity inside the interval, we have to split it in two integrals

$\int_{-1}^{0} x^{-\frac{1}{2}}dx+\int_{0}^{4} x^{-\frac{1}{2}}dx$

 

The integral $\int_{-1}^{0} x^{-\frac{1}{2}}dx$ results in: $-2\sqrt{-1}$

$-2\sqrt{-1}$

 

The integral $\int_{0}^{4} x^{-\frac{1}{2}}dx$ results in: $4$

$4$

 

Gather the results of all integrals

$-2\sqrt{-1}+4$

 

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

$-2i+4$

$-2i+4$

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