The expression for finding the area of the shaded region is:
- a$\int_2^8 (4 - \frac{x}{2} - 2) dx$
- b$\int_2^8 (\frac{x}{2} + 4) dx$
- c$\int_2^8 (\frac{y}{2} + 4) dy$
- d$\int_2^8 (4 - \frac{x}{2}) dx$
Answer
Answer
AIWritten by AI - it can contain mistakes.
Correct option: d
(d) $\int_2^8 (4 - \frac{x}{2}) dx$
The equation of the line is $x + 2y = 8 \Rightarrow 2y = 8 - x \Rightarrow y = 4 - \frac{x}{2}$.
The shaded region is bounded by the curve $y = 4 - \frac{x}{2}$, the line $x = 2$, the x-axis ($y = 0$), and extends to the x-intercept $x = 8$.
Therefore, the required area is $\int_2^8 (4 - \frac{x}{2}) dx$.
From ISC 2027 Specimen Mathematics Paper 1, question 1(viii).