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Mathematics · 2023 · 5 marks
CBSE 2023 · Region 1 · Set 3 · Q34
Find the area of the region bounded by the lines y=4 x+5, x+y=5 and 4 y=x+5, using integration.
Find the area of the region bounded by the lines $\displaystyle y=4 x+5, x+y=5$ and $\displaystyle 4 y=x+5$, using integration.
Marking-scheme solution
Correct Figure
Vertices are $\displaystyle \mathrm{A}(0,5), \mathrm{B}(-1,1), \mathrm{C}(3,2)$, Required area $\displaystyle =\int_{-1}^{0}(4 x+5) d x+\int_{0}^{3}(5-x) d x-\int_{-1}^{3} \frac{x+5}{4} d x$
$\displaystyle =\left.\frac{(4 x+5)^{2}}{8}\right|_{-1} ^{0}+\left.\frac{(5-x)^{2}}{-2}\right|_{0} ^{3}-\left.\frac{(x+5)^{2}}{8}\right|_{-1} ^{3}$
$\displaystyle =3+\frac{21}{2}-6=\frac{\mathbf{1 5}}{\mathbf{2}}$
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CBSE Class 12 Mathematics past-paper question from the 2023 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.