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

The integral from-3 to 1 of 3t^3+2t^2 is -124/3

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

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

- \frac{124}{3}

Decimal Notation

- 41.33333 \dots

Solution steps

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

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

\int_{- 3}^{1} 3 t^{3} d t = - 60

\int_{- 3}^{1} 2 t^{2} d t = \frac{56}{3}

= - 60 + \frac{56}{3}

Simplify

- 60 + \frac{56}{3} : - \frac{124}{3}

= - \frac{124}{3}

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What is the integral from-3 to 1 of 3t^3+2t^2 ?
The integral from-3 to 1 of 3t^3+2t^2 is -124/3