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What's the integral of sin(2x)?

Substitution. Let u = 2x, then du = 2dx.

The integral becomes ½ ∫ sin(u) du = -½ cos(u) + C

→ -½ cos(2x) + C

Why the ½?
When you substitute u = 2x, you get du = 2·dx, so dx = du/2. That ½ is the chain rule factor — it accounts for the inner derivative.
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Intro to Psychology, 11th Ed.

482 pages · Processed in 47s

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Ch. 3 — Sensation & Perception

Sensation is the process by which sensory receptors detect physical energy from the environment. Perception is the brain's interpretation of that sensory input. This chapter covers absolute thresholds, signal detection theory, Weber's law, and the organizational principles of Gestalt psychology...

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