Slide 4.8.pptx - Second Fundamental Theorem of Calculus...

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Second FundamentalTheorem of Calculus
Second Fundamental Theorem of CalculusIf f is continuous on [a,b] and F is any antiderivative of f thenOne can prove this using the 1st fundamental theorem.
Example 1Evaluate
Example 2EvaluateUse substitutionu = 4x + 1du = 4dxdx = du/4Change bounds of integralx = 6 → u = 4*6 + 1 = 25x = 12 → u= 4*12 + 1 = 49
TheoremLet f be continuous on [-a.a].1. If f is an even function,2. If f is an odd function,
Examples3. Evaluate4. Evaluate

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