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

The integral from 0 to 1 of 2+x^{1/3} is 11/4

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

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

\frac{11}{4}

Decimal

2.75

Solution steps

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

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

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

= 2 + \frac{3}{4}

Simplify

2 + \frac{3}{4} : \frac{11}{4}

= \frac{11}{4}

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What is the integral from 0 to 1 of 2+x^{1/3} ?
The integral from 0 to 1 of 2+x^{1/3} is 11/4