Calculating areas.

Question

The smallest code that gives the area between the curve p(x) = a₀ + a₁*x + a₂*x² + ..., the line y = 0, the line x = 0 and the line x = C

(i.e. something like this:

)

You can assume that p(x) >= 0 for x < C (bonus points if your code works for negative values of p(x)).

Input

C, a₀, a₁, ...

Output

a real number - the area

Example 1:

input: 2, 0, 1
output: 2.0

Examlpe 2:

input: 3.0, 0, 0.0, 2
output: 18

UPDATE:

• C > 0 is also assumed
• the area is between the curve, y=0, x=C and x = 0
• the input can be a list of any form; not necessarily comma separated.
• the output can be a real of any form (thus, '18' is a valid output, as is '18.0')

Answer 1

Mathematica: 48 Chars

.

Sum[#[[i+1]]#[[1]]^i/i,{i,Length@#-1}]&@Input[]

Answer 2

Python - 71 63 chars:

a=input()
print sum(1.*a[i]*a[0]**i/i for i in range(1,len(a)))

It's a simple integration of a polynomial function between 0 and C. And I haven't tested it, but I'm quite sure it works for negative values.

Answer 3

J, 26 characters

f=:3 :'((1}.y)&p.d._1)0{y'

eg.

   f 2 0 1
2
   f 3 0 0 2
18

Answer 4

Haskell, 85 characters

f(c:l)=sum.map(\(i,x)->x*c**i/i)$zip[1..]l
main=getLine>>=print.f.read.('[':).(++"]")

Answer 5

Ruby, 65 chars

i=s=0
c=gets(q=",").to_f
$<.each(q){|a|s+=a.to_f*c**(i+=1)/i}
p s

The code reads until the end of input, not the end of the line. So you need to hit Ctrl+d to terminate input (pipe the input in using echo or from a file).