Area under y = f(x): many thin vertical stripsy = f(x) के अंतर्गत क्षेत्रफल: अनेक पतली ऊर्ध्वाधर पट्टियाँy = f(x) ke neeche area: bahut saari patli vertical strips

NCERT Fig 8.1 · 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 y = f(x) (वक्र y = f(x)) — The top edge of the region. Here f(x) \ge 0, so the curve stays above the x-axis.
• Ordinate x = a (कोटि x = a) — The left wall of the region (the lower limit of the integral).
• Ordinate x = b (कोटि x = b) — The right wall of the region (the upper limit of the integral).
• Elementary strip (प्रारंभिक पट्टी) — A very thin rectangle of height y and width dx: its area is dA = y\,dx (the elementary area).
• Height of the strip = y (पट्टी की ऊँचाई = y) — From the x-axis up to the curve, so height = y = f(x).
• Width dx (चौड़ाई dx) — A tiny width along the x-axis. The thinner the strips, the more exact the total.
• Required area A (अभीष्ट क्षेत्रफल A) — Adding all the strips from a to b: A = \int_a^b y\,dx = \int_a^b f(x)\,dx.

Original diagram drawn by Simple Learning Hub, based on NCERT Fig 8.1. Report a mistake