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Popular Calculus >

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

Solution

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

Solution

\frac{14}{3}

+1

Decimal

4.66666 \dots

Solution steps

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

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

\int_{0}^{2} x^{2} d x = \frac{8}{3}

= 2 + \frac{8}{3}

Simplify

2 + \frac{8}{3} : \frac{14}{3}

= \frac{14}{3}

Graph

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Frequently Asked Questions (FAQ)

What is the integral from 0 to 2 of (1+x^2) ?
The integral from 0 to 2 of (1+x^2) is 14/3