where C is the constant of integration.
f(x, y, z) = x^2 + y^2 + z^2
from t = 0 to t = 1.
2.2 Find the area under the curve:
where C is the constant of integration.
y = Ce^(3x)
The area under the curve is given by:
dy/dx = 2x
y = ∫2x dx = x^2 + C
The gradient of f is given by:
3.1 Find the gradient of the scalar field:
∫[C] (x^2 + y^2) ds
from x = 0 to x = 2.
∇f = (∂f/∂x)i + (∂f/∂y)j + (∂f/∂z)k = 2xi + 2yj + 2zk
dy/dx = 3y