What is the integral from-2 to-1 of 2/(x^2) ?

The integral from-2 to-1 of 2/(x^2) is 1

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integral from-2 to-1 of 2/(x^2)

\int_{- 2}^{- 1} \frac{2}{x ^{2}} d x

1

Solution steps

\int_{- 2}^{- 1} \frac{2}{x ^{2}} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int_{- 2}^{- 1} \frac{1}{x ^{2}} d x

Apply the Power Rule

: [- \frac{1}{x}]_{- 2}^{- 1}

= 2 [- \frac{1}{x}]_{- 2}^{- 1}

Compute the boundaries:

\frac{1}{2}

= 2 \cdot \frac{1}{2}

Simplify

= 1

(4 x + 2 x^{- 1} y + 2 x^{- 1} y^{2}) d x + (1 + 2 y) d y = 0

f (x) = \frac{x}{( 1 + x ^{2} )}

2 y d x - x d y = 0

x^{2} - 6 x + 10

x \to 1 lim (x + 3)

What is the integral from-2 to-1 of 2/(x^2) ?
The integral from-2 to-1 of 2/(x^2) is 1