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Popular >

integral of k(1-x)

Solution

\int k (1 - x) d x

Solution

k (x - \frac{x ^{2}}{2}) + C

Solution steps

\int k (1 - x) d x

Take the constant out:

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

= k \cdot \int 1 - x 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

= k (\int 1 d x - \int x d x)

\int 1 d x = x

\int x d x = \frac{x ^{2}}{2}

= k (x - \frac{x ^{2}}{2})

Add a constant to the solution

= k (x - \frac{x ^{2}}{2}) + C

Popular Examples

integral of 15sin(x)

\int 15 sin (x) d x

integral of (sin(z)cos(z))/(1+sin^4(z))

\int \frac{sin ( z ) cos ( z )}{1 + sin ^{4} ( z )} d z

integral of a-x

\int a - x d x

integral of (x-2)/(sqrt(x+3))

\int \frac{x - 2}{x + 3} d x

integral of (5x^2-7x+4)

\int (5 x^{2} - 7 x + 4) d x

Frequently Asked Questions (FAQ)

What is the integral of k(1-x) ?
The integral of k(1-x) is k(x-(x^2)/2)+C