JEE 2023 — Mathematics PYQ
JEE | Mathematics | 2023The area bounded by the curves y=∣x−1∣+∣x−2∣ and y=3 is equal to 0.
Choose the correct answer:
- A.
5
(Correct Answer) - B.
4
- C.
6
- D.
3
5
Explanation
y = |x – 1| + |x – 2|
(i)\ -\infty < x < 1,\quad <br>y = -x + 1 - x + 2 = -2x + 3
(ii)\ 1 \le x < 2,\quad <br>y = (x-1) - (x-2) = x - 1 - x + 2 = 1
(iii)\ 2 \le x < \infty,\quad <br>y = x - 1 + x - 2 = 2x - 3
y=∣x−1∣+∣x−2∣=<br>⎩⎨⎧<br>−2x+3,<br>1,<br>2x−3,amp;−∞amp;1≤xamp;2≤xlt;xlt;2lt;∞<br>lt;1
Also y=3
Area=21(1+3)×2=4
Explanation
y = |x – 1| + |x – 2|
(i)\ -\infty < x < 1,\quad <br>y = -x + 1 - x + 2 = -2x + 3
(ii)\ 1 \le x < 2,\quad <br>y = (x-1) - (x-2) = x - 1 - x + 2 = 1
(iii)\ 2 \le x < \infty,\quad <br>y = x - 1 + x - 2 = 2x - 3
y=∣x−1∣+∣x−2∣=<br>⎩⎨⎧<br>−2x+3,<br>1,<br>2x−3,amp;−∞amp;1≤xamp;2≤xlt;xlt;2lt;∞<br>lt;1
Also y=3
Area=21(1+3)×2=4