Home › ACSEE (Form 6) › Advanced Mathematics › Numerical Methods › The area enclosed by $x^2+y^2=100$ with $x\ge0$ …
The area enclosed by $x^2+y^2=100$ with $x\ge0$ and $y\ge0$ is split into ten equal intervals. The correct limits and strip width are:
A$-10$ to $10$, $h=2$
B$0$ to $10$, $h=1$
C$0$ to $100$, $h=10$
D$-10$ to $10$, $h=1$
Answer & Solution
Correct answer: B. $0$ to $10$, $h=1$
1. The conditions $x\ge0$ and $y\ge0$ restrict the region to the first quadrant.
2. There the circle of radius $10$ runs from $x=0$ to $x=10$, so those are the limits.
3. Ten equal intervals over that range give $h=\dfrac{10-0}{10}=1$.
4. Taking $-10$ to $10$ ignores $x\ge0$ and doubles the region, which forces $h=2$ and a wrong area.
5. Limits of $0$ to $100$ confuse the radius squared with the radius.
_Source: NECTA ACSEE 2023 Advanced Mathematics 142/1, Question 7: Numerical Methods_