Calculus Examples

$v (t) = 4 \sin (t)$

Step 1

The function $V (t)$ can be found by finding the indefinite integral of the derivative $v (t)$ .

$V (t) = \int v (t) d t$

Step 2

Set up the integral to solve.

$V (t) = \int 4 \sin (t) d t$

Step 3

Since $4$ is constant with respect to $t$ , move $4$ out of the integral.

$4 \int \sin (t) d t$

Step 4

The integral of $\sin (t)$ with respect to $t$ is $- \cos (t)$ .

$4 (- \cos (t) + C)$

Step 5

Simplify the answer.

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Step 5.1

Simplify.

$4 (- \cos (t)) + C$

Step 5.2

Multiply $- 1$ by $4$ .

$- 4 \cos (t) + C$

Step 6

The answer is the antiderivative of the function $v (t) = 4 \sin (t)$ .

$V (t) =$ $- 4 \cos (t) + C$