What is the integral from 0 to 1 of 3-4x^2+3x^{3/4} ?

The integral from 0 to 1 of 3-4x^2+3x^{3/4} is 71/21

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integral from 0 to 1 of 3-4x^2+3x^{3/4}

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

\frac{71}{21}

Decimal

3.38095 \dots

Solution steps

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

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

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

\int_{0}^{1} 3 x^{\frac{3}{4}} d x = \frac{12}{7}

= 3 - \frac{4}{3} + \frac{12}{7}

Simplify

3 - \frac{4}{3} + \frac{12}{7} : \frac{71}{21}

= \frac{71}{21}

What is the integral from 0 to 1 of 3-4x^2+3x^{3/4} ?
The integral from 0 to 1 of 3-4x^2+3x^{3/4} is 71/21