integral of 7.9t-16.6 — step-by-step solution

Let's compute the integral:

\int (7.9 t - 16.6) d t

ⅰ

\int (7.9 t - 16.6) d t

\int 7.9 t d t - \int 16.6 d t

\int 7.9 t d t - \int 16.6 d t

ⓘ A constant factor stays in front of the integral. An antiderivative of x^n is x^(n+1)/(n+1), for n ≠ -1:

\int 7.9 t d t

7.9 \cdot \frac{t^{2}}{2}

■The derivative of

- 16.6 t

-16.6

, so

- 16.6 t

is an antiderivative of

-16.6

- \int 16.6 d t

- 16.6 t

7.9 \cdot \frac{t^{2}}{2} - 16.6 t

ⓘ Multiplying a fraction by a number multiplies its numerator:

7.9 \cdot \frac{t^{2}}{2}

\frac{7.9 t^{2}}{2}

■A fraction is simplified by dividing the numerator and the denominator by the same number:

\frac{7.9 t^{2}}{2}

3.95 t^{2}

3.95 t^{2} - 16.6 t

You can write the expression in factored form:

t \cdot (3.95 t - 16.6)

▶Indefinite integrals are defined up to an additive constant C, so this yields:

t \cdot (3.95 t - 16.6) + C