(Solved): Approximate the definite integral using the trapezoidal rule for the given value of n. Give the res ...

Approximate the definite integral using the trapezoidal rule for the given value of $$n$$. Give the result accurate to 3 decimal places. (a) $${?}_0^{?/2}\sin (x)dxn=6$$ (b) Find the upper bound for the absolute value of the error based on $$?f^{??}(x)?$$ and Theorem 1 . $$?E_T??$$ (c) Find the exact value of the definite integral. Theorem 1. If $$K$$ is a positive real number such that $$?f^{??}(x)??K$$ for all $$x$$ in $$[a,b]$$, then an upper bound for the absolute value of the error, $$E_T$$, in approximating $${?}_a^{b}f(x)\mathrm{d}x$$ using $$n$$ trapezoids is $$?E_T??\frac{K(b?a{)}^3}{12n^2}$$