Calculus Examples

$x = 2 y^{2}$ , $x = 0$ ; and $y = 3$

Step 1

Solve by substitution to find the intersection between the curves.

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Step 1.1

Replace all occurrences of $y$ with $3$ in each equation.

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Step 1.1.1

Replace all occurrences of $y$ in $x = 2 y^{2}$ with $3$ .

$x = 2 {(3)}^{2}$

$y = 3$

Step 1.1.2

Simplify the right side.

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Step 1.1.2.1

Simplify $2 {(3)}^{2}$ .

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Step 1.1.2.1.1

Raise $3$ to the power of $2$ .

$x = 2 \cdot 9$

$y = 3$

Step 1.1.2.1.2

Multiply $2$ by $9$ .

$x = 18$

$y = 3$

$x = 18$

$y = 3$

$x = 18$

$y = 3$

$x = 18$

$y = 3$

Step 1.2

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

$(18, 3)$

$(18, 3)$

Step 2

The area between the given curves is unbounded.

Unbounded area

Step 3

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$