Hi all,

it is quite hard for me to understand for part (c)

this is the question:

I have worked on part (b):

Basically just make integral from the interval [1,c] and find half the area of part (a)

\int_{1}^{c} \frac{1}{x^{2}} = \frac{5}{12}

I get the c=12/7

```
using Plots, LaTeXStrings, SymPy
gr()
x = collect(range(0, 4, length= 100))
f(x) = 1/(x^2)
function Area(f, a, b, n)
xs = a:(b-a)/n:b
deltas = diff(xs)
cs = xs[1:end-1]
sum(f(cs[i]) * deltas[i] for i in 1:length(deltas))
end
r1 = round(Area(x -> 1/(x^2), 1, 12/7, 50000), digits=5)
r2 = round(Area(x -> 1/(x^2), 12/7, 6, 50000), digits=5)
plot(f,0,7, xtick=1:5:6, xlims=(0,7), ylims=(0,1.2),
framestyle=:zerolines,
label=L"f(x) = \frac{1}{x^{2}}", legend=:topright)
# Fill the area
plot!(f,1,12/7, label="", fill=(0, 0.25, :blue))
plot!(f,12/7,6, label="", fill=(0, 0.45, :blue))
# The line that bisects the area vertically
plot!([12/7], seriestype="vline", color=:green, label="")
# Annotate the x line that bisects the area
annotate!([(12/7,-0.05, (L"x = \frac{12}{7}", 7, :blue))])
# Annotate the area
annotate!([(1.33,0.25, ("Left area =", 7, :black))])
annotate!([(1.3,0.15, (r1, 7, :black))])
annotate!([(2.23,0.05, ("Right area = ", 7, :black))])
annotate!([(2.97,0.05, (r2, 7, :black))])
```

then I try to work on part (c), the horizontal slicing, but the result is questionable, I still don’t understand

If I do this x = \frac{1}{\sqrt{y}}, and the interval will be [1/36,1], then the integral should be:

\int_{d}^{1} \frac{1}{\sqrt{y}} = \frac{5}{12}

I will get d=0.627, but when I calculate the integral for the area of this function in y terms:

it get the area of 20/12 \approx 1.66667

But the integral for area of this function in x terms get the total area of half the area in y terms:

it get the area of 10/12 \approx 0.8333

Which part is it that I am missing or lost?