Consider the line integral ∫_C F(r)·dr, with F(r) = x î + y ĵ + z k̂, where î, ĵ and k̂ are unit vectors in the (x,y,z) Cartesian coordinate system. The path C is given by r(t) = cos(t) î + sin(t) ĵ + t k̂, where 0 ≤ t ≤ π. The value of the integral, rounded off to 2 decimal places, is _________

Question

Accepted Answer

The correct answer is 4.91 to 4.95. GATE 2024 official key: 4.91 to 4.95. F·dr = d[½(x²+y²+z²)], a conservative field, so the integral = ½[(x²+y²+z²)]₀^π = ½[(1+π²)−1] = π²/2 ≈ 4.93.