Using horizontal strips, the area bounded by the curve $x = g(y)$, the…

Question

Using horizontal strips, the area bounded by the curve $x = g(y)$, the $y$-axis and the lines $y = c$ and $y = d$ is given by which integral?

Accepted Answer

B. $\int_c^d g(y)\,dy$

1. A horizontal elementary strip has width $x = g(y)$ and thickness $dy$, so $dA = x\,dy$.
2. Summing from $y = c$ to $y = d$ gives $A = \int_c^d x\,dy = \int_c^d g(y)\,dy$.
3. The variable of integration is $y$, ruling out forms written in $x$.
_Source: syllabus Mathematics Ch 8 "Application of Integrals", p.2_

Answer

$\int_c^d g(x)\,dx$

Answer

$\int_c^d y\,dx$

Answer

$\int_c^d g'(y)\,dy$

Using horizontal strips, the area bounded by the curve $x = g(y)$, the $y$-axis and the lines $y = c$ and $y = d$ is given by which integral?

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