3 years ago

What's the Y intercept of 3x + 4y = 5

1 answer:

5 0

Answer:6y

Step-by-step explanation:

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Irina-Kira [14]

The definition of the set E gives you a natural choice for the limits in the integral:

$\displaystyle \iiint_E y \, dV = \int_0^6 \int_0^x \int_{x-y}^{x+y} y \, dz \, dy \, dx$

Computing the integral, we get

$\displaystyle \iiint_E y \, dV = \int_0^6 \int_0^x y ((x+y)-(x-y)) \, dy \, dx = 2 \int_0^6 \int_0^x y^2 \, dy \, dx$

$\displaystyle \iiint_E y \, dV = 2 \int_0^6 \frac13 (x^3 - 0^3) \, dx = \frac23 \int_0^6 x^3 \, dx$

$\displaystyle \iiint_E y \, dV = \frac23 \cdot \frac14 (6^4 - 0^4) = \boxed{216}$

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2 years ago