Hi,
So I tried to calculate this integral at region D in the image, by splitting it to two integrals.
I got the wrong answer at the end:
\(\displaystyle \displaystyle \int_D \int\ 2 |\, x\, |\, -\, \sqrt{y\,}\, dxdy,\, \). . .\(\displaystyle D\, :\, \left\{\, y\, =\, x^2,\, y\, =\, x\, +\, 2\,\right\}\)
I thought of splitting the integral into:
\(\displaystyle \displaystyle \int_{-1}^{0}\, dx\, \int_{x^2}^{x+2}\, -2x\, -\, \sqrt{y\,}\, dy\, +\, \int_0^2\, dx\, \int_{x^2}^{x+2}\, 2x\, -\, \sqrt{y\,}\, dy\)
Did I split it right?
So I tried to calculate this integral at region D in the image, by splitting it to two integrals.
I got the wrong answer at the end:
\(\displaystyle \displaystyle \int_D \int\ 2 |\, x\, |\, -\, \sqrt{y\,}\, dxdy,\, \). . .\(\displaystyle D\, :\, \left\{\, y\, =\, x^2,\, y\, =\, x\, +\, 2\,\right\}\)
I thought of splitting the integral into:
\(\displaystyle \displaystyle \int_{-1}^{0}\, dx\, \int_{x^2}^{x+2}\, -2x\, -\, \sqrt{y\,}\, dy\, +\, \int_0^2\, dx\, \int_{x^2}^{x+2}\, 2x\, -\, \sqrt{y\,}\, dy\)
Did I split it right?
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