GATE 2026 PI – Question 34

Engineering Mathematics · Calculus · 1 mark · Numerical answer

Evaluate $\int_C(2x\,dx+2y\,dy+2z\,dz)$, where C is a semicircle in z = 0 starting at (0,0,0) and ending at (1,0,0). Give an integer.

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Correct answer: 1 to 1

Explanation

The integrand is the exact differential $d(x^2+y^2+z^2)$. The integral is path independent and equals the endpoint potential difference: $1^2-0^2=\mathbf1$.

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