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Popular >

integral from 0 to 1 of 3x-3x^2

Solution

\int_{0}^{1} 3 x - 3 x^{2} d x

Solution

\frac{1}{2}

+1

Solution steps

\int_{0}^{1} 3 x - 3 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

= \int_{0}^{1} 3 x d x - \int_{0}^{1} 3 x^{2} d x

\int_{0}^{1} 3 x d x = \frac{3}{2}

\int_{0}^{1} 3 x^{2} d x = 1

= \frac{3}{2} - 1

Simplify

\frac{3}{2} - 1 : \frac{1}{2}

= \frac{1}{2}

Popular Examples

integral from 0 to 4 of 2xe^{x^2}

\int_{0}^{4} 2 x e^{x^{2}} d x

integral from-x to x of e^{-u^2}

\int_{- x}^{x} e^{- u^{2}} d u

integral from pi/6 to pi of |cos(x)|

\int_{\frac{π}{6}}^{π} ∣ cos (x) ∣ d x

integral from 1 to 3 of (3x+1)

\int_{1}^{3} (3 x + 1) d x

integral from 0 to 4 of (2t^2+t^{3/2})

\int_{0}^{4} (2 t^{2} + t^{\frac{3}{2}}) d t

Frequently Asked Questions (FAQ)

What is the integral from 0 to 1 of 3x-3x^2 ?
The integral from 0 to 1 of 3x-3x^2 is 1/2