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

The integral from-3 to 1 of ((2x-2)(2x+2)) is 64/3

Popular >

integral from-3 to 1 of ((2x-2)(2x+2))

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

\frac{64}{3}

Decimal

21.33333 \dots

Solution steps

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

Apply Integration By Parts

: [(2 x + 2) (x^{2} - 2 x) - \int 2 (x^{2} - 2 x) d x]_{- 3}^{1}

= [(2 x + 2) (x^{2} - 2 x) - \int 2 (x^{2} - 2 x) d x]_{- 3}^{1}

\int 2 (x^{2} - 2 x) d x = 2 (\frac{x ^{3}}{3} - x^{2})

= [(2 x + 2) (x^{2} - 2 x) - 2 (\frac{x ^{3}}{3} - x^{2})]_{- 3}^{1}

Simplify

[(2 x + 2) (x^{2} - 2 x) - 2 (\frac{x ^{3}}{3} - x^{2})]_{- 3}^{1} : [\frac{1}{3} (4 x^{3} - 12 x)]_{- 3}^{1}

= [\frac{1}{3} (4 x^{3} - 12 x)]_{- 3}^{1}

Compute the boundaries:

\frac{64}{3}

= \frac{64}{3}

\int_{0}^{π} e^{x} sin (2 x) d x

\int_{\frac{π}{4}}^{π} sin^{5} (x) d x

\int_{0}^{1} x^{4} - x^{6} d x

\int_{7}^{14} x^{2} - 16 d x

\int_{1}^{10} \frac{x - 1}{x} d x

What is the integral from-3 to 1 of ((2x-2)(2x+2)) ?
The integral from-3 to 1 of ((2x-2)(2x+2)) is 64/3