How do you evaluate the definite integral $\int ∣ ∣ x^{3} + 64 ∣ ∣ d x$ $int|x^3+64| dx$ from $[- 8, 0]$ $[-8,0]$ ?

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How do you evaluate the definite integral $\int ∣ ∣ x^{3} + 64 ∣ ∣ d x$ $int|x^3+64| dx$ from $[- 8, 0]$ $[-8,0]$ ?

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Answer 1 · 2016-07-29T18:01:28

$896$ $896$

Explanation:

$f (x) = x^{3} + 64$ $f(x) = x^3+64$ changes sign for $x = - 4$ $x = -4$ so

$\int_{- 8}^{0} | f (x) | d x = - \int_{- 8}^{- 4} f (x) d x + \int_{- 4}^{0} f (x) d x$ $int_{-8}^0abs(f(x))dx = -int_{-8}^{-4}f(x)dx+int_{-4}^0f(x)dx$

but

$\int_{a}^{b} f (x) d x = 64 b + \frac{b^{4}}{4} - (64 a + \frac{a^{4}}{4})$ $int_a^bf(x)dx = 64 b + b^4/4-(64 a + a^4/4)$ then

$\int_{- 8}^{0} | f (x) | d x = 704 + 192 = 896$ $int_{-8}^0 abs(f(x))dx=704 + 192 = 896$

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How do you evaluate the definite integral $\int ∣ ∣ x^{3} + 64 ∣ ∣ d x$ $int|x^3+64| dx$ from $[- 8, 0]$ $[-8,0]$ ?

1 Answer

Explanation:

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How do you evaluate the definite integral ∫∣∣x3+64∣∣dxint|x^3+64| dx from [−8,0][-8,0]?

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Explanation:

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How do you evaluate the definite integral $\int ∣ ∣ x^{3} + 64 ∣ ∣ d x$ $int|x^3+64| dx$ from $[- 8, 0]$ $[-8,0]$ ?