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Determine whether the statement is true or false. Explain your answer.If $A(x)$ is the area under the graph of a nonnegative continuous function $f$ over an interval $[a, x],$ then $A^{\prime}(x)=f(x)$
True
Calculus 1 / AB
Calculus 2 / BC
Chapter 5
INTEGRATION
Section 1
An Overview of the Area Problem
Functions
Limits
Differentiation
Integrals
Integration
Integration Techniques
Continuous Functions
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So in this problem, the claim is the area under the curve will equal the function itself, right. And in this particular case, what we're looking at as long as the graph of a non negative, continuous function, which means that we've got some function that's above the X axis, then, yes, we're going to get a positive value here, and that positive value is going to be determined by the area under the curve. And so, in this particular case, over the interval, a prime of X will equal the function. So this is a true state.
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