# How do you use the trapezoidal rule to approximate the Integral from 0 to 0.5 of (1-x^2)^0.5 dx with n=4 intervals?

Oct 6, 2015

See the explanation section, below.

#### Explanation:

On $\left[a , b\right] = \left[0 , 0.5\right]$, with $n = 4$, we get

$\Delta x = \frac{b - a}{n} = \frac{0.5 - 0}{4} = 0.125$

The endpoints of the subintervals are found by beginning at $a = 0$ and successively adding $\Delta x$ to find the points.

${x}_{0} = 0$, ${x}_{1} = 0.125$, ${x}_{2} = 0.250$, ${x}_{3} = 0.375$,, ${x}_{4} = 0.5$

Now apply the formula (do the arithmetic):

${T}_{4} = \frac{\Delta x}{2} \left[f \left({x}_{0}\right) + 2 f \left({x}_{1}\right) + 2 f \left({x}_{2}\right) + 2 f \left({x}_{3}\right) + f \left({x}_{4}\right)\right]$