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Popular Calculus >

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

Solution

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

Solution

\frac{7}{3}

+1

Decimal

2.33333 \dots

Solution steps

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

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

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

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

= \frac{1}{3} + 1 + 1

Simplify

\frac{1}{3} + 1 + 1 : \frac{7}{3}

= \frac{7}{3}

Graph

Popular Examples

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\int_{1}^{4} \frac{1}{( 1 + x )} d x

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\int_{0}^{2} 3 x^{2} - 2 x + 7 e^{x} d x

integral from-2 to 1 of 1/x

\int_{- 2}^{1} \frac{1}{x} d x

integral from 1 to 5 of 5

\int_{1}^{5} 5 d x

integral from-2 to 3 of |x^2-1|

\int_{- 2}^{3} x^{2} - 1 d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 1 of x^2+2x+1 ?
The integral from 0 to 1 of x^2+2x+1 is 7/3