Area between x = g(y) and the y-axis: horizontal stripsx = g(y) और y-अक्ष के बीच क्षेत्रफल: क्षैतिज पट्टियाँx = g(y) aur y-axis ke beech area: horizontal strips

NCERT Fig 8.2 · 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.
• Curve x = g(y) (वक्र x = g(y)) — Here x is written in terms of y; the curve is the right edge of the region.
• Line y = c (रेखा y = c) — The bottom of the region (lower limit of \int dy).
• Line y = d (रेखा y = d) — The top of the region (upper limit of \int dy).
• Horizontal strip (क्षैतिज पट्टी) — Length x, height dy, so dA = x\,dy. It lies flat, from the y-axis to the curve.
• Length of the strip = x (पट्टी की लंबाई = x) — From the y-axis to the curve: x = g(y).
• Height dy (ऊँचाई dy) — A tiny step along the y-axis.
• Required area A (अभीष्ट क्षेत्रफल A) — A = \int_c^d x\,dy = \int_c^d g(y)\,dy.

Original diagram drawn by Simple Learning Hub, based on NCERT Fig 8.2. Report a mistake