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Popular >

integral from 0 to 1 of (x+3)^2

Solution

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

Solution

\frac{37}{3}

+1

Decimal Notation

12.33333 \dots

Solution steps

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

Expand

(x + 3)^{2} : x^{2} + 6 x + 9

= \int_{0}^{1} x^{2} + 6 x + 9 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} 6 x d x + \int_{0}^{1} 9 d x

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

\int_{0}^{1} 6 x d x = 3

\int_{0}^{1} 9 d x = 9

= \frac{1}{3} + 3 + 9

Simplify

\frac{1}{3} + 3 + 9 : \frac{37}{3}

= \frac{37}{3}

Popular Examples

integral from 1 to 3 of pi(ln(x))^2

\int_{1}^{3} π (ln (x))^{2} d x

integral from 1 to 2 of (1/x+x)

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

integral from 0 to 1 of 4-x

\int_{0}^{1} 4 - x d x

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

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

integral from 3 to 5 of x^{3/2}

\int_{3}^{5} x^{\frac{3}{2}} d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 1 of (x+3)^2 ?
The integral from 0 to 1 of (x+3)^2 is 37/3