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Popular >

integral of 2(1-x)

Solution

\int 2 (1 - x) d x

Solution

2 x - x^{2} + C

Solution steps

\int 2 (1 - x) d x

Take the constant out:

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

= 2 \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

= 2 (\int 1 d x - \int x d x)

\int 1 d x = x

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

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

Simplify

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

= 2 x - x^{2}

Add a constant to the solution

= 2 x - x^{2} + C

Popular Examples

integral of 2/3 x^{3/2}*1/x

\int \frac{2}{3} x^{\frac{3}{2}} \cdot \frac{1}{x} d x

integral of (xe^{-2x})

\int (x e^{- 2 x}) d x

y^{''}+16y=0,y(0)=2,y^'(0)=1

y^{^{''}} + 16 y = 0, y (0) = 2, y^{^{'}} (0) = 1

(\partial)/(\partial x)(arcsin(5x))

\frac{\partial}{\partial x} (arcsin (5 x))

y^{''''}+4y^{''}=0

y^{^{''''}} + 4 y^{^{''}} = 0

Frequently Asked Questions (FAQ)

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