et f(x) = 6x? on [(1, 3.5). a) Find L(f, P) and U(f, P) when P 3.5 p) Use calculus to evaluate 6x dx,

In this question, the concept of Riemann Integral is applied.

Riemann Integral

To estimate ${\int }_a^{b}f\left(x\right)dx$, Riemann sums are utilized by approximating areas using the areas of rectangles or trapezoids. The width of each rectangle/trapezoid is x. Different ways of approximation are available depending on how we choose the height of the rectangles, including the trapezoidal method.

The Left-Hand Rule, the Right-Hand Rule, and the Midpoint Rule are three standard methods for the height of these rectangles. The Left Hand Rule states that the function should be evaluated at the subinterval's left-hand endpoint and the rectangle should be that height.  The Right Hand Rule says to evaluate the function at the right endpoint on each subinterval and make the rectangle that height.