# Calculate Area of Function with Circumscribed Polygon with CalculusWithJulia

Hi all,

I try to calculate this function

` \$3x^{2} + x + 1\$`

But, I get the result different from the solution: This is the code I use:

``````using CalculusWithJulia

function riemann(f, a, b, n; method="right")
xs = a:(b-a)/n:b
deltas = diff(xs)      # forms x2-x1, x3-x2, ..., xn-xn-1
if method == "left"
cs = xs[1:end-1]
elseif method == "right"
cs = xs[2:end]
else
cs = [(xs[i] + xs[i+1])/2 for i in 1:length(deltas)]
end
sum(f(cs[i]) * deltas[i] for i in 1:length(deltas))
end

# intervals
a, b = -1,1
# the function
f(x) = 3x^2 + x + 1
#number of partitions
n = 10

# print the result
println("The area for \$f(x):")
riemann(f, -1, 1, 10)   # Same result
``````

the result from the code is: 4.24

different from the solution 4.656. Maybe the solution is wrong?

The solution is different. The left rectangle is a left sum, the right one a right sum (heights taken from f(-1) and f(1)). Try this to match:

``````riemann(f, -1, 0, 5; method="left") + riemann(f, 0, 1, 5; method="right")
``````
1 Like

Thanks @j_verzani , you are really a Mathematics expert!

The CalculusWithJulia is amazing!