Area under y = cos x from 0 to 2π = 1 + 2 + 1 = 4y = cos x के अंतर्गत 0 से 2π तक क्षेत्रफल = 1 + 2 + 1 = 4y = cos x ke neeche 0 se 2π tak area = 1 + 2 + 1 = 4

NCERT Example 4 (Fig 8.10) · 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 = \cos x (वक्र y = \cos x) — Positive on \left(0, \frac{\pi}{2}\right) and \left(\frac{3\pi}{2}, 2\pi\right), negative on \left(\frac{\pi}{2}, \frac{3\pi}{2}\right).
• Region OABO (क्षेत्र OABO) — \int_0^{\pi/2} \cos x\,dx = [\sin x]_0^{\pi/2} = 1.
• Region BCDB (below the axis) (क्षेत्र BCDB (अक्ष के नीचे)) — \int_{\pi/2}^{3\pi/2} \cos x\,dx = -1 - 1 = -2; area = |-2| = 2.
• Region DEFD (क्षेत्र DEFD) — \int_{3\pi/2}^{2\pi} \cos x\,dx = 0 - (-1) = 1. Total area = 1 + 2 + 1 = 4.
• A(0, 1) (A(0, 1)) — \cos 0 = 1.
• B\left(\frac{\pi}{2}, 0\right) (B\left(\frac{\pi}{2}, 0\right)) — \cos\frac{\pi}{2} = 0: the curve goes below the axis here.
• C(\pi, -1) (C(\pi, -1)) — \cos \pi = -1, the lowest point.
• D\left(\frac{3\pi}{2}, 0\right) (D\left(\frac{3\pi}{2}, 0\right)) — \cos\frac{3\pi}{2} = 0: the curve comes back above the axis.
• E(2\pi, 1) (E(2\pi, 1)) — \cos 2\pi = 1.
• F(2\pi, 0) (F(2\pi, 0)) — Foot of the ordinate x = 2\pi.
• Ordinate x = 2\pi (कोटि x = 2\pi) — Right boundary of the region.

Original diagram drawn by Simple Learning Hub, based on NCERT Example 4 (Fig 8.10). Report a mistake