List of top Engineering Mathematics Questions on Integration by trapezoidal and Simpson’s rules

If the trapezoidal rule with a single interval [0, 1] is exact for the approximate value of \( \int_0^1 (x^3 - cx^2) \, dx \). Then the value of \( c \).

A function $f(x)$, that is smooth and convex-shaped (concave downward) on the interval $(x_l,x_u)$ is shown. The function is observed at an odd number of regularly spaced points. If the area under the function is computed numerically, then