Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I am trying to integrate a region from $0$ to $1$ on the $x$-axis and from $x$ to $1$ on the $y$-axis which is like an upside-down triangle with edges on $y = 1$ and $x = 0$ and $y = x$ so I set up the integral as: $$\int_0^1 \int_x^1 dy\, dx $$ but when I plug the following code into Wolframalpha:

integrate from 0 to 1 integrate from x to 1 1 dy dx

it gives me the region in the first quadrant under the line $y = -x + 1$ (link to Wolfram Alpha page)

enter image description here

What am I doing wrong?

share|improve this question

2 Answers 2

up vote 1 down vote accepted

I suspect the incorrect region is just a problem with Wolfram Alpha. (Note however that $\frac{1}{2}$ is the correct value of the integral.) The correct region is of course

enter image description here

share|improve this answer
    
Thanks I got 1/2 for the answer too, my question was more on why is Wolframalpha's graph is so different from what I expected. Appreciate your clarification. –  Gaduss Feb 23 at 20:07

In this case it doesn't matter since you are integrating half of a square. More precisely, the upper half of the square with a line going cutting it in half diagonally. You know that for a square, $Area=4*length.$ So, just take half of that and you get your integral which is equal to $\frac12$.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.