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  3. let f(x) = x^3 ? x on [?1, 1]. find the true area

Let f(x) = x^3 ? x on [?1, 1]. Find the true area of the shaded...

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Basic Math

Let f(x) = x^3 ? x on [?1, 1].

Find the true area of the shaded region using a limit of Riemannsums, taking the sample points to be the left endpoints. Hint: toease the computations, you can use the fact that (a + b)^ 3 = a ^3+ 3a^2 b + 3ab^2 + b^3 (which follows by expanding the cube).

Verify your work by evaluating the corresponding definiteintegral using the FTC.

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