Calculus Examples

$x = y^{4}$ , $y = \sqrt{2 - x}$ , $y = 0$

Solve by substitution to find the intersection between the curves.

Tap for more steps...

Replace all occurrences of $y$ with $0$ in each equation.

Tap for more steps...

Replace all occurrences of $y$ in $x = y^{4}$ with $0$ .

$x = {(0)}^{4}$

$y = 0$

$y = \sqrt{2 - x}$

Simplify the right side.

Tap for more steps...

Raising $0$ to any positive power yields $0$ .

$x = 0$

$y = 0$

$y = \sqrt{2 - x}$

$x = 0$

$y = 0$

$y = \sqrt{2 - x}$

Replace all occurrences of $y$ in $y = \sqrt{2 - x}$ with $0$ .

$0 = \sqrt{2 - x}$

$x = 0$

$y = 0$

Simplify the left side.

Tap for more steps...

Remove parentheses.

$0 = \sqrt{2 - x}$

$x = 0$

$y = 0$

$0 = \sqrt{2 - x}$

$x = 0$

$y = 0$

$0 = \sqrt{2 - x}$

$x = 0$

$y = 0$

Replace all occurrences of $x$ with $0$ in each equation.

Tap for more steps...

Replace all occurrences of $x$ in $0 = \sqrt{2 - x}$ with $0$ .

$0 = \sqrt{2 - (0)}$

$x = 0$

$y = 0$

Simplify the right side.

Tap for more steps...

Simplify $\sqrt{2 - (0)}$ .

Tap for more steps...

Multiply $- 1$ by $0$ .

$0 = \sqrt{2 + 0}$

$x = 0$

$y = 0$

Add $2$ and $0$ .

$0 = \sqrt{2}$

$x = 0$

$y = 0$

$0 = \sqrt{2}$

$x = 0$

$y = 0$

$0 = \sqrt{2}$

$x = 0$

$y = 0$

$0 = \sqrt{2}$

$x = 0$

$y = 0$

Since $0 = \sqrt{2}$ is not true, there is no solution.

No solution

The area between the given curves is unbounded.

Unbounded area