Area function A(x) = ∫ₐˣ f(x) dxक्षेत्रफल फलन A(x) = ∫ₐˣ f(x) dxArea function A(x) = ∫ₐˣ f(x) dx

NCERT Fig 7.1 · Class 12 Maths · Chapter 7 · interactive diagram

Parts and what they mean

• Curve y = f(x) (वक्र y = f(x)) — A continuous function, here with f(x) > 0 on [a, b].
• Area function A(x) = \int_a^x f(x)\,dx (क्षेत्रफल फलन A(x) = \int_a^x f(x)\,dx) — The area from a up to the moving point x. First fundamental theorem: A'(x) = f(x).
• Rest of the area up to b (b तक का शेष क्षेत्रफल) — When x reaches b, A(b) = \int_a^b f(x)\,dx, the whole area.
• Lower limit a (निम्न सीमा a) — The fixed left edge of the region.
• Moving point x (चलता बिंदु x) — Slide x to the right and the shaded area A(x) grows at the rate f(x) — the height of the red line.
• Upper limit b (उच्च सीमा b) — The right end of the interval [a, b].
• 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 Fig 7.1. Report a mistake