Explain in one or two sentences why

MATHEMATICS · Subjective · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Explain in one or two sentences why, if

f(x)\ge 0

[a,b]

, the definite integral

\int_a^b f(x)\,dx

equals the geometric area enclosed by the curve

y=f(x)

, the

x

-axis, and the lines

x=a

and

x=b