Question

AYUDEMEN PORFA 3/4x²y-[3/4xy²+(1/5xy²-7/2x²y+2)]+5/3

Answer 1

Respuesta:

(17 x^2 y)/4 - (19 x y^2)/20 - 1/3

diferente metodos:

Roots for the variable y:

y = -(sqrt(15) sqrt(4335 x^4 - 304 x) - 255 x^2)/(114 x)

y = (sqrt(15) sqrt(4335 x^4 - 304 x) + 255 x^2)/(114 x)

Partial derivatives:

d/dx((17 x^2 y)/4 - (19 x y^2)/20 - 1/3) = 1/20 y (170 x - 19 y)

d/dy((17 x^2 y)/4 - (19 x y^2)/20 - 1/3) = 1/20 x (85 x - 38 y)

Indefinite integral:

integral(-1/3 + (17 x^2 y)/4 - (19 x y^2)/20) dx = (17 x^3 y)/12 - (19 x^2 y^2)/40 - x/3 + constant

Definite integral over a disk of radius R:

integral integral_(x^2 + y^2<R^2)((17 x^2 y)/4 - (19 x y^2)/20 - 1/3) dx dy = -(π R^2)/3

Definite integral over a square of edge length 2 L:

integral_(-L)^L integral_(-L)^L (-1/3 + (17 x^2 y)/4 - (19 x y^2)/20) dy dx = -(4 L^2)/3