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