What is the integral of-195sin(7.8t) ?

The integral of-195sin(7.8t) is 24.99999…cos(7.8t)+C

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integral of-195sin(7.8t)

\int - 195 sin (7.8 t) d t

24.99999 \dots cos (7.8 t) + C

Solution steps

\int - 195 sin (7.8 t) d t

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - 195 \cdot \int sin (7.8 t) d t

Apply u-substitution

: \int sin (u) \frac{1}{7.8} d u

= - 195 \cdot \int sin (u) \frac{1}{7.8} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - 195 \cdot \frac{1}{7.8} \cdot \int sin (u) d u

Simplify

= - 195 \cdot 0.12820 \dots \cdot \int sin (u) d u

Use the common integral:

\int sin (u) d u = - cos (u)

= - 195 \cdot 0.12820 \dots (- cos (u))

Substitute back

u = 7.8 t

= - 195 \cdot 0.12820 \dots (- cos (7.8 t))

Simplify

= 24.99999 \dots cos (7.8 t)

Add a constant to the solution

= 24.99999 \dots cos (7.8 t) + C

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What is the integral of-195sin(7.8t) ?
The integral of-195sin(7.8t) is 24.99999…cos(7.8t)+C