Vault Of Euclid

Area Under One Arch of the Sine Curve

Area and arc length warmup

Find the area under the arch of \( y = \sin x \) between \( x = 0 \) and \( x = \pi \).

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What you need first

The definition of the definite integral as the area under a curve
The Fundamental Theorem of Calculus
The antiderivative of the sine function
Basic trigonometric values (cosine of 0 and pi)

What this problem tests

Tests the ability to set up a basic definite integral for area and evaluate it using standard trigonometric antiderivatives.

This is a classic introductory problem in Calculus I when learning about the definite integral and its geometric interpretation as area.

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