Quick questions on Areas between curves (SACE Stage 2 Mathematical Methods)

Q: What are step 1 - intersections?

Set x^2=x+2: $x^2-x-2=0 (x-2)(x+1)=0 x=-1,\ 2.$

Q: What is step 3 - integrate?

$A=_-1^2((x+2)-x^2)\,dx=[x^22+2x-x^33]_-1^2.$

2short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What are step 1 - intersections?

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Set

x^2=x+2

: $

x^2-x-2=0 \quad\Rightarrow\quad (x-2)(x+1)=0 \quad\Rightarrow\quad x=-1,\ 2.

What is step 3 - integrate?

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A=\int_{-1}^{2}\big((x+2)-x^2\big)\,dx=\Big[\tfrac{x^2}{2}+2x-\tfrac{x^3}{3}\Big]_{-1}^{2}.

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