Chapter 4: Integration
Section 4.2: The Definite Integral
By evaluating an appropriate definite integral, obtain the area above the x-axis, but under the graph of fx=6+x−x2,x∈−2,3.
The astute reader will note that the requisite area was obtained in Example 4.1.1 as the limit of a left Riemann sum. Here, the area is obtained via the Definite Integral template in the Calculus palette.
Define the function f
Context Panel: Assign Function
fx=6+x−x2→assign as functionf
Area via the definite integral
Expression palette: Definite Integral template
Context Panel: Evaluate and Display Inline
∫−23fx ⅆx = 1256
The fields of the definite integral template are traversed by use of the Tab key. If the polynomial rule for the function f is to appear as the integrand, the typical calculus text would enclose the terms in parentheses. However, Maple treats the integral sign and the differential dx as the bounds on the integrand and will display and evaluate integrals without parentheses.
∫−236+x−x2 ⅆx = 1256
Of course, it would always be possible to type the appropriate parentheses into the Definite Integral template.
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