∫(2x^2 + 3x - 1) dx = (2/3)x^3 + (3/2)x^2 - x + C
The line integral is given by:
Solution:
∫(2x^2 + 3x - 1) dx
3.2 Evaluate the line integral:
y = ∫2x dx = x^2 + C
∫[C] (x^2 + y^2) ds
∫[C] (x^2 + y^2) ds = ∫[0,1] (t^2 + t^4) √(1 + 4t^2) dt
2.2 Find the area under the curve:
The area under the curve is given by:
The gradient of f is given by:
where C is the curve: