Calculus Examples

$\int_{0}^{3} 35 e^{t} d t$

Step 1

Since $35$ is constant with respect to $t$ , move $35$ out of the integral.

$35 \int_{0}^{3} e^{t} d t$

Step 2

The integral of $e^{t}$ with respect to $t$ is $e^{t}$ .

$35 (e^{t}]_{0}^{3})$

Step 3

Substitute and simplify.

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Step 3.1

Evaluate $e^{t}$ at $3$ and at $0$ .

$35 ((e^{3}) - e^{0})$

Step 3.2

Simplify.

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Step 3.2.1

Anything raised to $0$ is $1$ .

$35 (e^{3} - 1 \cdot 1)$

Step 3.2.2

Multiply $- 1$ by $1$ .

$35 (e^{3} - 1)$

Step 4

Simplify.

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Step 4.1

Apply the distributive property.

$35 e^{3} + 35 \cdot - 1$

Step 4.2

Multiply $35$ by $- 1$ .

$35 e^{3} - 35$

Step 5

The result can be shown in multiple forms.

Exact Form:

$35 e^{3} - 35$

Decimal Form:

$667.99379231 \dots$

Step 6