Calculus Examples

$\int_{0}^{2} [\frac{7}{\sin^{2} (x) + \cos^{2} (x)} - 4 e] d x$

Step 1

Remove parentheses.

$\int_{0}^{2} \frac{7}{\sin^{2} (x) + \cos^{2} (x)} - 4 e d x$

Step 2

Simplify.

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Step 2.1

Factor $1$ out of $\frac{7}{\sin^{2} (x) + \cos^{2} (x)} - 4 e$ .

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Step 2.1.1

Factor $1$ out of $\frac{7}{\sin^{2} (x) + \cos^{2} (x)}$ .

$\int_{0}^{2} 1 \frac{7}{\sin^{2} (x) + \cos^{2} (x)} - 4 e d x$

Step 2.1.2

Factor $1$ out of $- 4 e$ .

$\int_{0}^{2} 1 \frac{7}{\sin^{2} (x) + \cos^{2} (x)} + 1 (- 4 e) d x$

Step 2.1.3

Factor $1$ out of $1 \frac{7}{\sin^{2} (x) + \cos^{2} (x)} + 1 (- 4 e)$ .

$\int_{0}^{2} 1 (\frac{7}{\sin^{2} (x) + \cos^{2} (x)} - 4 e) d x$

Step 2.2

Apply pythagorean identity.

$\int_{0}^{2} 1 (\frac{7}{1} - 4 e) d x$

Step 2.3

Multiply $\frac{7}{1} - 4 e$ by $1$ .

$\int_{0}^{2} \frac{7}{1} - 4 e d x$

Step 2.4

Divide $7$ by $1$ .

$\int_{0}^{2} 7 - 4 e d x$

Step 3

Apply the constant rule.

$(7 - 4 e) x]_{0}^{2}$

Step 4

Substitute and simplify.

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Step 4.1

Evaluate $(7 - 4 e) x$ at $2$ and at $0$ .

$((7 - 4 e) \cdot 2) - (7 - 4 e) \cdot 0$

Step 4.2

Simplify.

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Step 4.2.1

Move $2$ to the left of $7 - 4 e$ .

$2 \cdot (7 - 4 e) - (7 - 4 e) \cdot 0$

Step 4.2.2

Multiply $0$ by $- 1$ .

$2 (7 - 4 e) + 0 (7 - 4 e)$

Step 4.2.3

Multiply $0$ by $7 - 4 e$ .

$2 (7 - 4 e) + 0$

Step 4.2.4

Add $2 (7 - 4 e)$ and $0$ .

$2 (7 - 4 e)$

Step 5

Simplify.

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Step 5.1

Apply the distributive property.

$2 \cdot 7 + 2 (- 4 e)$

Step 5.2

Multiply $2$ by $7$ .

$14 + 2 (- 4 e)$

Step 5.3

Multiply $- 4$ by $2$ .

$14 - 8 e$

Step 6

The result can be shown in multiple forms.

Exact Form:

$14 - 8 e$

Decimal Form:

$- 7.74625462 \dots$