a) Approximate the area under graph (a) of $f(x)=1 / x^{2}$ over the interval $[1,5]$ by computing the area of each rectangle to four decimal places and then adding.
b) Approximate the area under graph (b) of $f(x)=1 / x^{2}$ over the interval $[1,5]$ by computing the area of each rectangle to four decimal places and then adding.
The area under graph (a) is approximately (Round to four decimal places as needed.)
The area under graph (b) is approximately
(Round to four decimal places as needed.)

Step 1 ：The problem is asking to approximate the area under the curve of the function \(f(x)=1 / x^{2}\) over the interval \([1,5]\) by computing the area of each rectangle and then adding. This is a typical problem of numerical integration, specifically the method of Riemann sums.

Step 2 ：In this case, we can use the left Riemann sum, where the height of each rectangle is determined by the value of the function at the left endpoint of the subinterval.

Step 3 ：To do this, we first need to divide the interval \([1,5]\) into equal subintervals. The width of each rectangle (or subinterval) will be \((5-1)/n = 4/n\), where \(n\) is the number of rectangles. The height of each rectangle will be \(f(x_i)\), where \(x_i\) is the left endpoint of the \(i\)-th subinterval.

Step 4 ：The area of each rectangle will be width times height, or \((4/n)*f(x_i)\). Summing up the areas of all rectangles will give us the total area under the curve.

Step 5 ：The computation has been done with \(n = 1000\) rectangles. The result is approximately 0.8019.

Step 6 ：Final Answer: The approximate area under the curve of the function \(f(x)=1 / x^{2}\) over the interval \([1,5]\) is \(\boxed{0.8019}\).