GATE 2016 EC – Question 36
The integral $\frac{1}{2\pi} \iint_D (x + y + 10) \, dx \, dy$, where $D$ denotes the disc: $x^2 + y^2 \leq 4$, evaluates to ________
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 18 to 22
Explanation
By symmetry the integrals of $x$ and $y$ over the disc are both 0. The constant term gives $10 \times (\text{area of disc}) = 10 \times \pi \times 2^2 = 40\pi$. Dividing by $2\pi$ gives $20$.