(Solved): please do the trapezoidal rule along with the midpoint and i will upvote.  Estimate \( \int_{0} ...

Estimate \( \int_{0}^{1} 4 \cos \left(x^{2}\right) d x \) using the following, rule with \( n=4 \). the Trapezoldal Rule Step 1 The Trapezoldal Rule says that \[ \int_{a}^{b} f(x) d x \approx T_{n}=\frac{\Delta x}{2}\left[f\left(x_{0}\right)+2 f\left(x_{1}\right)+\cdots+2 f\left(x_{n}-1\right)+f\left(x_{n}\right)\right] . \] We need to estimate \( \int_{0}^{1} 4 \cos \left(x^{2}\right) d x \) with \( n=4 \) subintervals. We have Therefore, \[ \frac{\Delta x}{2}= \] Step 2 We know that \( x_{0} \) represents the beginning of the first subinterval, so \( x_{0}= \) of the second subinterval), and so \( x_{1}= \)