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Warm up Problems 1. 2. 3.
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More With Integrals It can be helpful to guess and adjust Ex.
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Thm. Fundamental Theorem of Calculus If f (x) is a continuous function on [a,b], and if F(x) = f (x), then - F(x) is an antiderivative of f (x). - Find an antiderivative, then plug in the endpoints
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Ex.
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Pract.
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-Don’t write “+ c” on definite integrals -We could use a calculator to get the answer, but this way we get the exact answer, not just a decimal approximation
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Ex. Let R be the region bounded by, the x-axis, x = 1, and x = 4. Find a value for h so that the line x = h splits R into two regions of equal area.
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Def. A differential equation is an equation that involves a function and some of its derivatives. Ex. y = 3y - 5y 2 Ex. Let, find the general solution.
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Ex. Solve the IVP if y(1) = 3. Def. An initial value problem (IVP) is a differential equation and a value of the solution.
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