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Popular >

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

Solution

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

Solution

\frac{32}{3}

+1

Decimal

10.66666 \dots

Solution steps

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

\int_{- 3}^{1} 3 d x = 12

\int_{- 3}^{1} 2 x d x = - 8

\int_{- 3}^{1} x^{2} d x = \frac{28}{3}

= 12 - (- 8) - \frac{28}{3}

Simplify

12 - (- 8) - \frac{28}{3} : \frac{32}{3}

= \frac{32}{3}

Graph

Popular Examples

integral from 2 to 4 of |x-3|

\int_{2}^{4} ∣ x - 3 ∣ d x

integral from-1 to 2 of 4x^2

\int_{- 1}^{2} 4 x^{2} d x

integral from 3 to 4 of x^2-x-6

\int_{3}^{4} x^{2} - x - 6 d x

integral from 0 to 2 of xe^{3x}

\int_{0}^{2} x e^{3 x} d x

integral from 9 to 10 of (x-10)^9

\int_{9}^{10} (x - 10)^{9} d x

Frequently Asked Questions (FAQ)

What is the integral from-3 to 1 of 3-2x-x^2 ?
The integral from-3 to 1 of 3-2x-x^2 is 32/3