I am trying to solve this expression using trapeze rule. $ $ \int_0^1(1+x)\ln^2(1+x)dx$ $
So at the beginning I am dividing into five equal parts:
0-0.2, 0.2-0.4, 0.4-0.6, 0.6-0.8, 0.8-1
After that I calculate the value for those points using my
f(x) = (1 + x)ln^2(1+x) f(0) = (1 + 0)ln^2(1+0) = 0 f(0.2) = (1 + 0.2)ln^2(1+0.2) = 0.0398 f(0.4) = (1 + 0.4)ln^2(1+0.4) = 0.1584 f(0.6) = (1 + 0.6)ln^2(1+0.6) = 0.3534 f(0.8) = (1 + 0.8)ln^2(1+0.8) = 0.6218 f(1) = (1 + 1)ln^2(1+1) = 0.9609
Now I am using this pattern to calculate the approximate value of the integral.
=0.2*(0.9609/2+0.0398+0.1584+0.3534+0.6218) = 0.3307
I wanted to check if value i got is correct, so i visited Wolfarm Alpha. I put there my expression and I got
Which result is correct?
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