Odd function: equal areas with opposite signsविषम फलन: बराबर क्षेत्रफल, विपरीत चिह्नOdd function: barabar area, ulte sign

NCERT P₇ (ii) · Class 12 Maths · Chapter 7 · interactive diagram

Parts and what they mean

• y = x^3, an odd function (y = x^3, एक विषम फलन) — f(-x) = (-x)^3 = -x^3 = -f(x): the graph is symmetric about the origin.
• Part below the x-axis (counts negative) (x-अक्ष के नीचे का भाग (ऋणात्मक गिना जाता है)) — On [−a, 0] the curve is below the axis, so this part of the integral is negative.
• Part above the x-axis (counts positive) (x-अक्ष के ऊपर का भाग (धनात्मक गिना जाता है)) — Same size as the red part but positive, so \int_{-a}^{a} x^3\,dx = 0.
• Symmetric limits −a and a (सममित सीमाएँ −a और a) — For an odd function, \int_{-a}^{a} f(x)\,dx = 0 (P₇ ii).
• 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 P₇ (ii). Report a mistake