What is the integral from 0 to 1 of 2x^2+2x+1 ?

The integral from 0 to 1 of 2x^2+2x+1 is 8/3

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integral from 0 to 1 of 2x^2+2x+1

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

\frac{8}{3}

Decimal

2.66666 \dots

Solution steps

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

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

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

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

= \frac{2}{3} + 1 + 1

Simplify

\frac{2}{3} + 1 + 1 : \frac{8}{3}

= \frac{8}{3}

\int_{0}^{π} x \cdot cos (2 x) d x

\int_{0}^{2 π} 9 d θ

\int_{0}^{1} (1 - x^{2})^{\frac{- 1}{2}} d x

\int_{0}^{1} 6 x 4 x^{2} + 1 d x

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

What is the integral from 0 to 1 of 2x^2+2x+1 ?
The integral from 0 to 1 of 2x^2+2x+1 is 8/3