P₄: f(x) and f(a − x) enclose the same area on [0, a]P₄: [0, a] पर f(x) और f(a − x) समान क्षेत्रफल घेरते हैंP₄: [0, a] par f(x) aur f(a − x) same area gherte hain

NCERT P₄ · Class 12 Maths · Chapter 7 · interactive diagram

Parts and what they mean

• y = f(x) (y = f(x)) — Here f(x) = 0.18x^2 + 0.5 on [0, 4].
• y = f(a - x) (y = f(a - x)) — The same curve read from the other end: its mirror image in the line x = a/2.
• Mirror line x = a/2 (दर्पण रेखा x = a/2) — Reflecting in this line swaps x and a − x.
• Area under y = f(x) (y = f(x) के नीचे का क्षेत्रफल) — A reflection does not change area, so \int_0^a f(x)\,dx = \int_0^a f(a - x)\,dx.
• Upper limit a (उच्च सीमा a) — Here a = 4.
• 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.

Original diagram drawn by Simple Learning Hub, based on NCERT P₄. Report a mistake