Evaluate This Integral Containing a Piecewise Function.

Evaluate This Integral Containing a Piecewise Function.
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Please see the image for the problem. I am unfamiliar with integrating piecewise functions correctly, so I would like verification for this problem. Did I get the correct answer?

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Maya Lin-Takahashi
Author

Maya Lin-Takahashi

Maya is a hardware enthusiast who tests and reviews smart home devices, smartphones, wearables, and audio gear. She focuses on practical consumer value and build quality.