Input |
(8 x + 3 y + 67)/sqrt(8^2 + 3^2) |
Result |
(8 x + 3 y + 67)/sqrt(73) |
Geometric figure |
plane |
Real root |
y = -(8 x)/3 – 67/3 |
Root |
y = -(8 x)/3 – 67/3 |
Integer root |
x = 3 n + 1, y = -8 n – 25, n element Z |
Root for the variable y |
y = -(8 sqrt(73) x + 67 sqrt(73))/(3 sqrt(73)) |
Derivative |
(d)/(dx)((8 x + 3 y + 67)/sqrt(8^2 + 3^2)) = 8/sqrt(73) |
Indefinite integral |
integral (67 + 8 x + 3 y)/sqrt(73) dx = (4 x^2 + 3 x y + 67 x)/sqrt(73) + constant |
Definite integral over a disk of radius R |
integral integral_(x^2 + y^2
|
Definite integral over a square of edge length 2 L |
integral_(-L)^L integral_(-L)^L (67 + 8 x + 3 y)/sqrt(73) dy dx = (268 L^2)/sqrt(73) |