# How do you Use the trapezoidal rule with n=10 to approximate the integral int_0^2sqrt(x)*e^(-x)dx?

Nov 14, 2014

Let $f \left(x\right) = \sqrt{x} {e}^{- x} = \frac{\sqrt{x}}{e} ^ x$.

$\Delta x = \frac{b - a}{n} = \frac{2 - 0}{10} = 0.2$

By summing up the areas of trapezoids shown below,

we have

${T}_{10} = \left[f \left(0\right) + 2 f \left(0.2\right) + 2 f \left(0.4\right) + \cdots + 2 f \left(1.8\right) + f \left(2\right)\right] \frac{\Delta x}{2} \approx 0.64$

I hope that this was helpful.