integral of 1-x — step-by-step solution

Let's compute the integral:

\int (1 - x) d x

ⅰ

\int (1 - x) d x

\int 1 d x - \int x d x

\int 1 d x - \int x d x

ⓘ The derivative of

x

1

, so

x

is an antiderivative of

1

\int 1 d x

x

■An antiderivative of x^n is x^(n+1)/(n+1), for n ≠ -1:

- \int x d x

- \frac{x^{2}}{2}

x - \frac{x^{2}}{2}

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

- \frac{x^{2}}{2} + x + C