When the curve goes below the x-axis: Area = |A₁| + A₂जब वक्र x-अक्ष के नीचे जाए: क्षेत्रफल = |A₁| + A₂Jab curve x-axis ke neeche jaaye: Area = |A₁| + A₂

NCERT Fig 8.3, 8.4 · 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)) — On the left part f(x) < 0 (below the axis), on the right part f(x) > 0.
• Piece below the axis, A_1 < 0 (अक्ष के नीचे का भाग, A_1 < 0) — Its integral comes out negative. Area is never negative, so we take |A_1|.
• Piece above the axis, A_2 > 0 (अक्ष के ऊपर का भाग, A_2 > 0) — Its integral is positive and is used as it is. Total area A = |A_1| + A_2.
• Point where the curve crosses the x-axis (बिंदु जहाँ वक्र x-अक्ष को काटता है) — Find it by solving f(x) = 0, and split the integral at this point.
• Ordinate x = a (कोटि x = a) — Left boundary of the region.
• Ordinate x = b (कोटि x = b) — Right boundary of the region.

Original diagram drawn by Simple Learning Hub, based on NCERT Fig 8.3, 8.4. Report a mistake