y = 3x + 2 between x = −1 and x = 1: one piece below, one abovex = −1 और x = 1 के बीच y = 3x + 2: एक भाग नीचे, एक ऊपरx = −1 aur x = 1 ke beech y = 3x + 2: ek part neeche, ek upar
NCERT Example 3 (Fig 8.9) · Class 12 Maths · Chapter 8 · interactive diagram
Parts and what they mean
- x-axis (x-अक्ष) — The horizontal number line; inputs x are read here.
- y-axis (y-अक्ष) — The vertical number line; outputs y = f(x) are read here.
- Origin O(0, 0) (मूल बिंदु O(0, 0)) — Where the two axes cross.
- Line y = 3x + 2 (रेखा y = 3x + 2) — It meets the x-axis where 3x + 2 = 0, i.e. x = -\frac{2}{3}.
- Region ACBA (below the x-axis) (क्षेत्र ACBA (x-अक्ष के नीचे)) — \int_{-1}^{-2/3}(3x + 2)\,dx = -\frac{1}{6}, so its area is \left|-\frac{1}{6}\right| = \frac{1}{6}.
- Region ADEA (above the x-axis) (क्षेत्र ADEA (x-अक्ष के ऊपर)) — \int_{-2/3}^{1}(3x + 2)\,dx = \frac{25}{6}. Total area = \frac{1}{6} + \frac{25}{6} = \frac{13}{3}.
- A\left(-\frac{2}{3}, 0\right) (A\left(-\frac{2}{3}, 0\right)) — Where the line crosses the x-axis: split the integral here.
- B(-1, -1) (B(-1, -1)) — On the line at x = -1: y = 3(-1) + 2 = -1.
- C(-1, 0) (C(-1, 0)) — Foot of the ordinate x = -1 on the x-axis.
- D(1, 5) (D(1, 5)) — On the line at x = 1: y = 3(1) + 2 = 5.
- E(1, 0) (E(1, 0)) — Foot of the ordinate x = 1 on the x-axis.
- Ordinate x = -1 (कोटि x = -1) — Left boundary (lower limit).
- Ordinate x = 1 (कोटि x = 1) — Right boundary (upper limit).
Original diagram drawn by Simple Learning Hub, based on NCERT Example 3 (Fig 8.9). Report a mistake