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

 Exercise

$\int_{-1}^4\left(xu^{-\frac{1}{2}}\right)du$

 

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

$\int_{-1}^{0} xu^{-\frac{1}{2}}du+\int_{0}^{4} xu^{-\frac{1}{2}}du$

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The integral $\int_{-1}^{0} xu^{-\frac{1}{2}}du$ results in: $\left(-2\sqrt{-1}\right)x$

$\left(-2\sqrt{-1}\right)x$

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

$4x$

 

Gather the results of all integrals

$\left(-2\sqrt{-1}\right)x+4x$

 

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

$x\left(-2i\right)+4x$

$x\left(-2i\right)+4x$

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