Calculus Examples

$\int_{- 2}^{1} [(2 - x) - x^{2}] d y$

Step 1

Remove parentheses.

$\int_{- 2}^{1} (2 - x) - x^{2} d y$

Step 2

Apply the constant rule.

$(2 - x - x^{2}) y]_{- 2}^{1}$

Step 3

Substitute and simplify.

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Step 3.1

Evaluate $(2 - x - x^{2}) y$ at $1$ and at $- 2$ .

$((2 - x - x^{2}) \cdot 1) - (2 - x - x^{2}) \cdot - 2$

Step 3.2

Simplify.

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Step 3.2.1

Multiply $2 - x - x^{2}$ by $1$ .

$2 - x - x^{2} - (2 - x - x^{2}) \cdot - 2$

Step 3.2.2

Multiply $- 2$ by $- 1$ .

$2 - x - x^{2} + 2 (2 - x - x^{2})$

Step 4

Simplify.

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Step 4.1

Simplify each term.

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Step 4.1.1

Apply the distributive property.

$2 - x - x^{2} + 2 \cdot 2 + 2 (- x) + 2 (- x^{2})$

Step 4.1.2

Simplify.

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Step 4.1.2.1

Multiply $2$ by $2$ .

$2 - x - x^{2} + 4 + 2 (- x) + 2 (- x^{2})$

Step 4.1.2.2

Multiply $- 1$ by $2$ .

$2 - x - x^{2} + 4 - 2 x + 2 (- x^{2})$

Step 4.1.2.3

Multiply $- 1$ by $2$ .

$2 - x - x^{2} + 4 - 2 x - 2 x^{2}$

Step 4.2

Add $2$ and $4$ .

$- x - x^{2} + 6 - 2 x - 2 x^{2}$

Step 4.3

Subtract $2 x$ from $- x$ .

$- 3 x - x^{2} + 6 - 2 x^{2}$

Step 4.4

Subtract $2 x^{2}$ from $- x^{2}$ .

$- 3 x - 3 x^{2} + 6$

Step 5