What is the geometric interpretation of ∫[a to b] f(x) dx if f(x) ≥ 0? A. The slope of the curve y = f(x) between a and b B. The length of the curve y = f(x) from a to b C. The volume of a solid formed by rotating f(x) D. The area bounded by y = f(x), the x-axis, and lines x = a, x = b Answer: D) The area bounded by y = f(x), the x-axis, and lines x = a, x = b Explanation: For a non-negative function, the definite integral represents the area under the curve bounded by the x-axis and the vertical lines x = a and x = b.

imo class 12 definite integration

What is the geometric interpretation of ∫[a to b] f(x) dx if f(x) ≥ 0?

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What is the geometric interpretation of ∫[a to b] f(x) dx if f(x) ≥ 0?

A. The slope of the curve y = f(x) between a and b
B. The length of the curve y = f(x) from a to b
C. The volume of a solid formed by rotating f(x)
D. The area bounded by y = f(x), the x-axis, and lines x = a, x = b

Answer: D) The area bounded by y = f(x), the x-axis, and lines x = a, x = b

Explanation: For a non-negative function, the definite integral represents the area under the curve bounded by the x-axis and the vertical lines x = a and x = b.

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