What is the integral from 0 to 2 of 3x^3-2x^2-e^x ?

The integral from 0 to 2 of 3x^3-2x^2-e^x is -e^2+23/3

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integral from 0 to 2 of 3x^3-2x^2-e^x

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

- e^{2} + \frac{23}{3}

Decimal

0.27761 \dots

Solution steps

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

\int_{0}^{2} 3 x^{3} d x = 12

\int_{0}^{2} 2 x^{2} d x = \frac{16}{3}

\int_{0}^{2} e^{x} d x = e^{2} - 1

= 12 - \frac{16}{3} - (e^{2} - 1)

Simplify

12 - \frac{16}{3} - (e^{2} - 1) : - e^{2} + \frac{23}{3}

= - e^{2} + \frac{23}{3}

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\int_{2 π}^{3 π} sin (x) d x

What is the integral from 0 to 2 of 3x^3-2x^2-e^x ?
The integral from 0 to 2 of 3x^3-2x^2-e^x is -e^2+23/3