Question

Calculate the double integral. (30x2y3 − 25y4) da, r = {(x, y) | 0 ≤ x ≤ 1, 0 ≤ y ≤ 1} r

Answer 1

Answer:

-2.5

Step-by-step explanation:

We want to evaluate the double integral,

$\int \int _R (30x^2y^3-25y^4)dA$

where R is the rectangular region bounded by R={(x, y) | 0 ≤ x ≤ 1, 0 ≤ y ≤ 1}

We apply the limits to obtain;

$\int_0^1 \int _0^1 (30x^2y^3-25y^4)dxdy$

We evaluate the inner integral by integrating with respect to x whiles treating y as a constant.

$\int_0^1 (10x^3y^3-25y^4x)_0^1dy$

This gives us,

$\int_0^1 (10y^3-25y^4)dy$

We evaluate the resulting integral now to obtain;

$10(\frac{y^4}{4})-25(\frac{y^5}{5})|_0^1$

$2.5y^4-5y^5|_0^1=2.5-5=-2.5$