Question

Evaluate the following as true or false. The approximate value of a definite integral that is obtained using the trapezoidal rule will always be greater than the exact value of the same definite integral.

a. True
b. False

Answer 1

False. Let f(x) be an integrable function that is concave on an interval [a, b] in its domain. "Concave" here means that the secant line drawn from (a, f(a)) to (b, f(b)) lies below the graph of f(x).