Calculus Examples

$f' (t) = 82 (1 - e^{- 0.12 \cdot 8})$

Step 1

The function $f (t)$ can be found by evaluating the indefinite integral of the derivative $f' (t)$ .

$f (t) = \int f' (t) d t$

Step 2

Multiply $- 0.12$ by $8$ .

$\int 82 (1 - e^{- 0.96}) d t$

Step 3

Apply the constant rule.

$82 (1 - e^{- 0.96}) t + C$

Step 4

Rewrite $82 (1 - e^{- 0.96}) t + C$ as $82 (1 - \frac{1}{e^{0.96}}) t + C$ .

$82 (1 - \frac{1}{e^{0.96}}) t + C$

Step 5

The function $f$ if derived from the integral of the derivative of the function. This is valid by the fundamental theorem of calculus.

$f (t) = 82 (1 - \frac{1}{e^{0.96}}) t + C$