Original
Suppose {{MATH_238}} is the (continuous) velocity function of an object traveling along a straight line during the interval {{MATH_239}}, which has position function {{MATH_240}}.
The displacement of the object can be found in two ways:
{{CMD_241}}
{{CMD_242}} As {{MATH_243}} and
{{CMD_244}} As a definite integral {{MATH_245}}.
{{CMD_246}}
In particular, the definite integral of a velocity function can be calculated by finding
the distance function:
{{MATH_247}}
{{CMD_248}}