X}} \right){\rm{dx}} = \frac{{\rm{h}}}{2}\left[ {{{\rm{y}}_{\rm{o}}} + {{\rm{y}}_{\rm{n}}} + 2\left( {{{\rm{y}}_1} + {{\rm{y}}_2} + {{\rm{y}}_3}{\rm{\;}} \ldots } \right)} \right]\)Calculation:GIVEN:f(0) = 1, f(1) = 2.72 and h = 1, ∴ n = 1.xx0 = 0x1 = 1y = f(x)Y0 = 1y1 = 2.72\(I =\mathop \smallint \limits_0^1 f\left( x \right)dx \Rightarrow \frac h2 [y_0 +y_n ]=\frac{1}{2}[1\;+\;2.72]\Rightarrow 1.86\)

"> X}} \right){\rm{dx}} = \frac{{\rm{h}}}{2}\left[ {{{\rm{y}}_{\rm{o}}} + {{\rm{y}}_{\rm{n}}} + 2\left( {{{\rm{y}}_1} + {{\rm{y}}_2} + {{\rm{y}}_3}{\rm{\;}} \ldots } \right)} \right]\)Calculation:GIVEN:f(0) = 1, f(1) = 2.72 and h = 1, ∴ n = 1.xx0 = 0x1 = 1y = f(x)Y0 = 1y1 = 2.72\(I =\mathop \smallint \limits_0^1 f\left( x \right)dx \Rightarrow \frac h2 [y_0 +y_n ]=\frac{1}{2}[1\;+\;2.72]\Rightarrow 1.86\)

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The f(0) = 1 and f(1) = 2.72, then the trapezoidal rule gives the approximate value of \(\mathop \smallint \limits_0^1 f\left( x \right)dx\) as

General Knowledge General Awareness in General Knowledge . 6 months ago

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Concept:where, b = upper limit, a = lower limit, h = step sizeAccording to the trapezoidal rule\(\mathop \smallint \limits_{\rm{a}}^{\rm{b}} {\rm{f}}\left( {\rm{X}} \right){\rm{dx}} = \frac{{\rm{h}}}{2}\left[ {{{\rm{y}}_{\rm{o}}} + {{\rm{y}}_{\rm{n}}} + 2\left( {{{\rm{y}}_1} + {{\rm{y}}_2} + {{\rm{y}}_3}{\rm{\;}} \ldots } \right)} \right]\)Calculation:GIVEN:f(0) = 1, f(1) = 2.72 and h = 1, ∴ n = 1.xx0 = 0x1 = 1y = f(x)Y0 = 1y1 = 2.72\(I =\mathop \smallint \limits_0^1 f\left( x \right)dx \Rightarrow \frac h2 [y_0 +y_n ]=\frac{1}{2}[1\;+\;2.72]\Rightarrow 1.86\)

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