Question

`int_a^b f(x) dx = int_a^b f (t) dt`

Options

• True

• False

Answer 1

The statement is true.

Explanation:

The equality holds because the integral of a function over an interval [a,b] does not depend on the variable used to represent the function's input. Whether we use x, t, or any other symbol, the integral's value remains the same as long as the function f and the limits of integration a and b are unchanged. This is a property of definite integrals, reflecting that they calculate the net area under the curve of f from a to b, which is independent of the variable of integration's notation.