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

\frac{- 8 x}{y} = 0

x \to 1 lim (x^{3} (5 - x))

x \to 1 lim (x^{\frac{1}{1 - x}})

n = 1 \sum \infty n (\frac{2}{3})^{n}

y = sin (x), y = x, x = \frac{π}{2}, x = π

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