Calculus Examples

$\int_{0}^{1} x^{- 2} d x$

Step 1

By the Power Rule, the integral of $x^{- 2}$ with respect to $x$ is $- x^{- 1}$ .

$- x^{- 1}]_{0}^{1}$

Step 2

Substitute and simplify.

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Step 2.1

Evaluate $- x^{- 1}$ at $1$ and at $0$ .

$(- 1^{- 1}) + 0^{- 1}$

Step 2.2

Simplify.

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Step 2.2.1

One to any power is one.

$- 1 \cdot 1 + 0^{- 1}$

Step 2.2.2

Multiply $- 1$ by $1$ .

$- 1 + 0^{- 1}$

Step 2.2.3

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$- 1 + \frac{1}{0}$

Step 2.2.4

The expression contains a division by $0$ . The expression is undefined.

Undefined

$- 1 + \frac{1}{0}$

Step 2.3

The expression contains a division by $0$ . The expression is undefined.

Undefined

$- 1 + \frac{1}{0}$

Step 3

The expression contains a division by $0$ . The expression is undefined.

Undefined