Ordinates are the vertical coordinates of points in a Cartesian plane. They represent the y-values in an ordered pair (x, y) and measure the distance from the x-axis. Positive ordinates lie above the x-axis and negative ordinates lie below. They help in graphing functions and analyzing mathematical relationships in coordinate geometry.
Class 12 Maths Chapter 8 Applications of Integrals is an important topic for the CBSE Exam 2024-25. It focuses on finding areas bounded by curves and calculating volumes of solids. It helps in solving real-life problems related to physics and engineering. Understanding these concepts is essential for higher studies and practical applications.
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The area bounded by the curve y = cos x, the x-axis, and the given ordinates x = π/2 and x = π is given by the definite integral:
A = ∫[π/2 to π] cos x dx
Evaluating the integral:
∫ cos x dx = sin x
Applying the limits:
A = sin(π) – sin(π/2)
= 0 – 1
= -1
Since area cannot be negative, we take the absolute value:
A = 1 square unit
Thus, the correct answer is: 1 sq. unit
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