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in Definite Integrals by (30.0k points)
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Evaluate the following Integral: 

\(\int\limits_{1/3}^{1}\cfrac{(\text x-\text x^3)^{1/3}}{\text x^4}d\text x \)

1 Answer

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Best answer

Let I = \(\int\limits_{1/3}^{1}\cfrac{(\text x-\text x^3)^{1/3}}{\text x^4}d\text x \)

Put \(\cfrac{1}{\text x^2}\) - 1 = t

⇒ –2x -2-1dx = dt (Differentiating both sides)

So, the new limits are 8 and 0.

Substituting this in the original integral,

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