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Question

Mathematics Question on Area between Two Curves

The area of the bounded region enclosed by the curve
y=3−∣x−12∣−∣x+1∣y=3−|x−\frac{1}{2}|−|x+1|
and the x-axis is

A

94\frac{9}{4}

B

4516\frac{45}{16}

C

278\frac{27}{8}

D

6316\frac{63}{16}

Answer

278\frac{27}{8}

Explanation

Solution

The correct answer is (C) : 278\frac{27}{8}

Fig.

y={2x−72x<−1 32−1≤x≤12 52−2xx>12y = \begin{cases} 2x-\frac{7}{2} & x < -1 \\\ \frac{3}{2} & -1 \leq x \leq \frac{1}{2} \\\ \frac{5}{2} - 2x & x > \frac{1}{2} \end{cases}
y=3−∣x−12∣−∣x+1∣y=3−|x−\frac{1}{2}|−|x+1|
Area of shaded region (required area) =12(3+32)⋅32=278\frac{1}{2}(3+\frac{3}{2})⋅\frac{3}{2}=\frac{27}{8}