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Popular >

integral of 2(x-2)

Solution

\int 2 (x - 2) d x

Solution

x^{2} - 4 x + C

Solution steps

\int 2 (x - 2) d x

Take the constant out:

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

= 2 \cdot \int x - 2 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

= 2 (\int x d x - \int 2 d x)

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

\int 2 d x = 2 x

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

Simplify

2 (\frac{x ^{2}}{2} - 2 x) : x^{2} - 4 x

= x^{2} - 4 x

Add a constant to the solution

= x^{2} - 4 x + C

Popular Examples

integral of cos(t-x)

\int cos (t - x) d x

derivative of f(x)=7x-5 derivative of

f (x) = 7 x - 5

integral of (2x+4)^2

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

derivative of 1/(ln(2))

\frac{d}{d x} (\frac{1}{ln ( 2 )})

tangent of y=(7x)/(x-1),(2,14)tangent of

y = \frac{7 x}{x - 1}, (2, 14)

Frequently Asked Questions (FAQ)

What is the integral of 2(x-2) ?
The integral of 2(x-2) is x^2-4x+C