Chapter 4: Integration

Section 4.2: The Definite Integral

Example 4.2.3

a)  Obtain the value of the definite integral ${\int }_{-1}^2\left(x^3-7 x^2\+5 x\+4\right) \mathit{\ⅆ}x$ as the limit of a right Riemann sum. b)  Verify the result by using Maple to evaluate the definite integral. Solution Define the function $f$  •  Write $f\left(x\right)\=\dots$  Context Panel: Assign Function $f\left(x\right)\=x^3-7 x^2\+5 x\+4$$\stackrel{\text{assign as function}}{\to }$$f$ Part (a) Define the stepsize $h$  •  Context Panel: Evaluate and Display Inline •  Context Panel: Assign to a Name≻$h$  $\frac{2-\left(-1\right)}{n}$ = $\frac{3}{n}$$\stackrel{\text{assign to a name}}{\to }$$h$ Obtain the limit of the right Riemann sum •  Expression palette: Limit template Expression palette: Summation template •  Context Panel: Evaluate and Display Inline $\underset{n\to \infty }{lim}\sum _{k\=1}^{n}f\left(-1\+k h\right) h$ = $\frac{9}{4}$ Part (b) Evaluate the definite integral in Maple •  Expression palette: Definite Integral template •  Context Panel: Evaluate and Display Inline ${\int }_{-1}^2\left(x^3-7 x^2\+5 x\+4\right) \mathit{\ⅆ}x$ = $\frac{9}{4}$

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