What is the integral from-1 to 3 of-x^3+3x^2+1 ?

The integral from-1 to 3 of-x^3+3x^2+1 is 12

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

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

12

Solution steps

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

\int_{- 1}^{3} x^{3} d x = 20

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

\int_{- 1}^{3} 1 d x = 4

= - 20 + 28 + 4

Simplify

= 12

\int_{2}^{8} (5 x^{2} + 3 x + 5) d x

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

\int_{x}^{x^{2}} \frac{1}{t ^{3} + 2} d t

\int_{1}^{3} - \frac{1}{4} x + 5 d x

\int_{0}^{8} 4 d x

What is the integral from-1 to 3 of-x^3+3x^2+1 ?
The integral from-1 to 3 of-x^3+3x^2+1 is 12