What is the integral from 0 to 1 of 2-x^2-x^4 ?

The integral from 0 to 1 of 2-x^2-x^4 is 22/15

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integral from 0 to 1 of 2-x^2-x^4

\int_{0}^{1} 2 - x^{2} - x^{4} d x

\frac{22}{15}

Decimal

1.46666 \dots

Solution steps

\int_{0}^{1} 2 - x^{2} - x^{4} 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 d x - \int_{0}^{1} x^{2} d x - \int_{0}^{1} x^{4} d x

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

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

\int_{0}^{1} x^{4} d x = \frac{1}{5}

= 2 - \frac{1}{3} - \frac{1}{5}

Simplify

2 - \frac{1}{3} - \frac{1}{5} : \frac{22}{15}

= \frac{22}{15}

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What is the integral from 0 to 1 of 2-x^2-x^4 ?
The integral from 0 to 1 of 2-x^2-x^4 is 22/15