How do you evaluate the definite integral $\int \frac{1}{x^{2}} d x$ $int 1/x^2 dx$ from $[2, 3]$ $[2,3]$ ?

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How do you evaluate the definite integral $\int \frac{1}{x^{2}} d x$ $int 1/x^2 dx$ from $[2, 3]$ $[2,3]$ ?

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Answer 1 · 2016-09-25T13:08:47

$\frac{1}{6}$ $1/6$

Explanation:

Rewrite this as:

$\int_{2}^{3} x^{- 2} d x$ $int_2^3x^-2dx$

Use the power rule for integration to tackle this: $\int x^{n} d x = \frac{x^{n + 1}}{n + 1}$ $intx^ndx=x^(n+1)/(n+1)$

$= {[\frac{x^{- 2 + 1}}{- 2 + 1}]}_{2}^{3}$ $=[x^(-2+1)/(-2+1)]_2^3$

$= {[\frac{x^{- 1}}{- 1}]}_{2}^{3}$ $=[x^-1/(-1)]_2^3$

$= {[- \frac{1}{x}]}_{2}^{3}$ $=[-1/x]_2^3$

$= - \frac{1}{3} - (- \frac{1}{2})$ $=-1/3-(-1/2)$

$= \frac{1}{6}$ $=1/6$

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How do you evaluate the definite integral $\int \frac{1}{x^{2}} d x$ $int 1/x^2 dx$ from $[2, 3]$ $[2,3]$ ?

1 Answer

Explanation:

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How do you evaluate the definite integral $\int \frac{1}{x^{2}} d x$ $int 1/x^2 dx$ from $[2, 3]$ $[2,3]$ ?