What is the integral from-2 to 2 of x^3-2x^2+7 ?

The integral from-2 to 2 of x^3-2x^2+7 is 52/3

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integral from-2 to 2 of x^3-2x^2+7

\int_{- 2}^{2} x^{3} - 2 x^{2} + 7 d x

\frac{52}{3}

Decimal

17.33333 \dots

Solution steps

\int_{- 2}^{2} x^{3} - 2 x^{2} + 7 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_{- 2}^{2} x^{3} d x - \int_{- 2}^{2} 2 x^{2} d x + \int_{- 2}^{2} 7 d x

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

\int_{- 2}^{2} 2 x^{2} d x = \frac{32}{3}

\int_{- 2}^{2} 7 d x = 28

= 0 - \frac{32}{3} + 28

Simplify

0 - \frac{32}{3} + 28 : \frac{52}{3}

= \frac{52}{3}

\int_{1}^{4} 8 d x

\int_{- 1}^{2} x^{3} - 4 x d x

\int_{1}^{4} 2^{3 x} d x

\int_{- 7}^{7} \frac{t ^{3}}{11 + 8 t ^{2}} d t

\int_{- 7}^{7} 7^{2} - x^{2} d x

What is the integral from-2 to 2 of x^3-2x^2+7 ?
The integral from-2 to 2 of x^3-2x^2+7 is 52/3