What is the integral from 0 to x of q(1-x/L) ?

The integral from 0 to x of q(1-x/L) is q(x-(x^2)/(2L))

Popular >

integral from 0 to x of q(1-x/L)

\int_{0}^{x} q (1 - \frac{x}{L}) d x

q (x - \frac{x ^{2}}{2 L})

Solution steps

\int_{0}^{x} q (1 - \frac{x}{L}) d x

Take the constant out:

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

= q \cdot \int_{0}^{x} 1 - \frac{x}{L} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= q (\int_{0}^{x} 1 d x - \int_{0}^{x} \frac{x}{L} d x)

\int_{0}^{x} 1 d x = x

\int_{0}^{x} \frac{x}{L} d x = \frac{x ^{2}}{2 L}

= q (x - \frac{x ^{2}}{2 L})

\int_{2}^{6} (x^{2} - 4 x) d x

\int_{1}^{2} x x^{2} - 2 d x

\int_{1}^{x} ln (y) d y

\int_{0}^{\frac{1}{2}} (cos (π x) - 2^{x}) d x

\int_{0}^{1} (e^{t} - e + 1)^{2} d t

What is the integral from 0 to x of q(1-x/L) ?
The integral from 0 to x of q(1-x/L) is q(x-(x^2)/(2L))