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Differentiate w.r.t. y
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\int y^{2}\mathrm{d}x
Evaluate the indefinite integral first.
y^{2}x
Find the integral of y^{2} using the table of common integrals rule \int a\mathrm{d}x=ax.
y^{2}\times 3-y^{2}
The definite integral is the antiderivative of the expression evaluated at the upper limit of integration minus the antiderivative evaluated at the lower limit of integration.
2y^{2}
Simplify.