Calculus Examples

$y = x^{2}$

Step 1

Solve by substitution to find the intersection between the curves.

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Step 1.1

Eliminate the equal sides of each equation and combine.

$x^{2} = 0$

Step 1.2

Solve $x^{2} = 0$ for $x$ .

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Step 1.2.1

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{0}$

Step 1.2.2

Simplify $\pm \sqrt{0}$ .

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Step 1.2.2.1

Rewrite $0$ as $0^{2}$ .

$x = \pm \sqrt{0^{2}}$

Step 1.2.2.2

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 0$

Step 1.2.2.3

Plus or minus $0$ is $0$ .

$x = 0$

Step 1.3

Substitute $0$ for $x$ .

$y = 0$

Step 1.4

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(0, 0)$

Step 2

The area between the given curves is unbounded.

Unbounded area

Step 3