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Popular Calculus >

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

Solution

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

Solution

\frac{5}{24}

+1

Decimal

0.20833 \dots

Solution steps

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

\int_{0}^{\frac{1}{2}} 2 x^{2} d x = \frac{1}{12}

\int_{0}^{\frac{1}{2}} x d x = \frac{1}{8}

= \frac{1}{12} + \frac{1}{8}

Simplify

\frac{1}{12} + \frac{1}{8} : \frac{5}{24}

= \frac{5}{24}

Graph

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Frequently Asked Questions (FAQ)

What is the integral from 0 to 1/2 of 2x^2+x ?
The integral from 0 to 1/2 of 2x^2+x is 5/24