The approximate value of $\int_2 x^2 d x$ by using trapezoidal rule with 4 equal intervals, is

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Aicharya · Accepted Answer

Here, $\begin{aligned} n=4, h=\frac{9-1}{4}=2 \ y_0=f(1)=(1)^2=1 \ y_1=f(3)=(3)^2=9 \ y_2=f(5)=(5)^2=25 \ y_3=f(7)=(7)^2=49 \ y_4=f(9)=(9)^2=81 \end{aligned}$ by trapezoidal rule $\begin{aligned} \int_1^9 x^2 d x & =\frac{h}{2}\left[y_0+2\left(y_1+y_2+y_3ight)+y_4ight] \ & =\frac{1}{2} \cdot 2[1+2(9+25+49)+81]=248 \end{aligned}$

The approximate value of $\int_2 x^2 d x$ by using trapezoidal rule with 4 equal intervals, is

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