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## Main Question or Discussion Point

I was wondering if you guys could help me understand something. I have an equation that, when I graph it, looks a lot like a regular sine function. However, when I integrate it to find the area under it and graph the new function, I'm getting a negative result in the first 0.56 radians or so.

The equation is:

dy = xSIN(x) - 0.03356(x^2)SIN(x) dx

Integrating for x (actually, letting Wolfram Mathematica Online Integrator do it for me), I get:

y = (1 - 0.06712x)SIN(x) + 0.03356(x - 29.8643)(x + 0.0669695)COS(x)

(I'm trying to analyze this for x = 0 to pi, by the way.)

The first equation gives me nothing negative, so why when it's integrated and graphed do I get a negative dip before x = 0.56?

The equation is:

dy = xSIN(x) - 0.03356(x^2)SIN(x) dx

Integrating for x (actually, letting Wolfram Mathematica Online Integrator do it for me), I get:

y = (1 - 0.06712x)SIN(x) + 0.03356(x - 29.8643)(x + 0.0669695)COS(x)

(I'm trying to analyze this for x = 0 to pi, by the way.)

The first equation gives me nothing negative, so why when it's integrated and graphed do I get a negative dip before x = 0.56?