Antiderivatives Visually via Accumulation

In this installment of synthwave and math, we sketch the net accumulation curves of elementary functions by measuring the directed, signed area between the curve and the x-axis. This means that area above the x-axis, moving from left to right, is positive. If you move from right to left it is negative, and then these switch below the x-axis. We use these accumulation functions to state general antiderivative rules. Along with various rules (like substitution and integration by parts, etc.) and chain rules, these rules help you find a variety of antiderivatives. If you want proof that these are the correct derivatives, you should consult any standard calculus text.

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For a related video with derivatives, check out:
   • Elementary Derivative Rules Graphically | ...  

For more math and synthwave, check out:
   • Synthwave Mathematics  

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