Math 22 Area and the Fundamental Theorem of Calculus

Definition of a Definite Integral

 Let $f$ be nonnegative and continuous on the closed interval $[a,b]$. 
 The area of the region bounded by the graph of $f$, the x-axis, 
 and the lines $x=a$ and Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle x=b}
 is denoted by
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \text{Area}=\int_a^b f(x)dx}

 
 The expression Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int_a^b f(x)dx}
 is called the definite integral from a to b, 
 where a is the lower limit of integration and b is the upper limit of integration.

The Fundamental Theorem of Calculus

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