Calculus Examples

$y = x^{3}$ , $y = x^{2} - 1$

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.

$x^{3} = x^{2} - 1$

Step 1.2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx - 0.75487766 + y = x^{2} - 1$

Step 1.3

Evaluate $y$ when $x = - 0.75487766$ .

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Step 1.3.1

Substitute $- 0.75487766$ for $x$ .

$y = {(- 0.75487766)}^{2} - 1$

Step 1.3.2

Simplify ${(- 0.75487766)}^{2} - 1$ .

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Step 1.3.2.1

Raise $- 0.75487766$ to the power of $2$ .

$y = 0.56984029 - 1$

Step 1.3.2.2

Subtract $1$ from $0.56984029$ .

$y = - 0.4301597$

Step 1.4

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

$(- 0.75487766, - 0.4301597)$

Step 2

The area between the given curves is unbounded.

Unbounded area

Step 3