Explain why the definite integral may fail to equal the geometric area between the…

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

Problem

Explain why the definite integral ∫abf(x) dx\int_a^b f(x)\,dx may fail to equal the geometric area between the curve y=f(x)y=f(x) and the x-axis when f(x)f(x) takes both positive and negative values on [a,b][a,b].

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