What is the integral from 0 to 1 of 2sqrt(x)-2x ?

The integral from 0 to 1 of 2sqrt(x)-2x is 1/3

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integral from 0 to 1 of 2sqrt(x)-2x

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

\frac{1}{3}

Decimal Notation

0.33333 \dots

Solution steps

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

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

\int_{0}^{1} 2 x d x = \frac{4}{3}

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

= \frac{4}{3} - 1

Simplify

\frac{4}{3} - 1 : \frac{1}{3}

= \frac{1}{3}

\int \frac{x ^{3} - 1}{x ^{4} - 4 x + 1} d x

\frac{d y}{d x} + (\frac{3}{x}) y = - 2 x - 7

3 sin (x), 4 cos (x), [0, 0.8 π]

\frac{d}{d x} (- 4 sec^{2} (x) + 6 sec^{4} (x))

x \to 3 lim (- 3 x - 7)

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