examday

/TMUA

Use the trapezium rule to approximate the value of the following definite integral, with the number of intervals $n=4$:

The following lines are the attempt to solve this integral. Which is the first incorrect line?

• I. The step size $h$ is $\dfrac{5\pi-\pi}{4}=\pi$.
• II. Then, we can get the intermediate points and the boundary points: $x_0=\pi$, $x_1=2\pi$, $x_2=3\pi$, $x_3=4\pi$, $x_4=5\pi$.
• III. By applying the trapezium rule: $S=\dfrac12\bigl(f(\pi)+f(2\pi)+f(3\pi)+f(4\pi)+f(5\pi)\bigr)$
• IV. Finally, we get the exact solution: $S=\dfrac12(\pi+2\pi+3\pi+4\pi+5\pi)=\dfrac{15}{2}\pi$