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Popular >

integral from 0 to 4 of-x^2+2x+3

Solution

\int_{0}^{4} - x^{2} + 2 x + 3 d x

Solution

\frac{20}{3}

+1

Decimal Notation

6.66666 \dots

Solution steps

\int_{0}^{4} - x^{2} + 2 x + 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}^{4} x^{2} d x + \int_{0}^{4} 2 x d x + \int_{0}^{4} 3 d x

\int_{0}^{4} x^{2} d x = \frac{64}{3}

\int_{0}^{4} 2 x d x = 16

\int_{0}^{4} 3 d x = 12

= - \frac{64}{3} + 16 + 12

Simplify

- \frac{64}{3} + 16 + 12 : \frac{20}{3}

= \frac{20}{3}

Popular Examples

integral from-infinity to 0 of xe^{-10x}

\int_{- \infty}^{0} x e^{- 10 x} d x

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\int_{- π}^{π} sin (x) cos (3 x) d x

integral from 0 to 0.2 of 5(1-e^{-2t})

\int_{0}^{0.2} 5 (1 - e^{- 2 t}) d t

integral from 0 to 1 of 1/(6x+2)

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

integral from 9 to 16 of-x^{-1/2}+5

\int_{9}^{16} - x^{- \frac{1}{2}} + 5 d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 4 of-x^2+2x+3 ?
The integral from 0 to 4 of-x^2+2x+3 is 20/3