Check the solution to "Evaluate the ff, improper integrals. ∫1∞1x3dx"

glamrockqueen7

Answered question

2021-05-29

Evaluate the ff, improper integrals.

\int_{1}^{\infty} \frac{1}{x^{3}} d x

cheekabooy

Skilled2021-05-30Added 83 answers

Step 1
The objective is to evaluate the given improper integrals:

\int_{1}^{\infty} \frac{1}{x^{3}} d x

Step 2
Evaluate the given integral as:

\int_{1}^{\infty} \frac{1}{x^{3}} d x = [\int \frac{1}{x^{3}} d x]_{1}^{\infty}

= [\frac{x^{- 3 + 1}}{- 3 + 1}]_{1}^{\infty} = [\frac{1}{- 2 x^{2}}]_{1}^{\infty} = [0 + \frac{1}{2 \times 1^{2}}]

= \frac{1}{2}

Thus,

\int_{1}^{\infty} \frac{1}{x^{3}} d x = \frac{1}{2}

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