How do you evaluate the definite integral $\int (- 2 x^{2} + 4 x + 2) d x$ $int(-2x^2+4x+2)dx$ from $[0, 3]$ $[0,3]$ ?

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How do you evaluate the definite integral $\int (- 2 x^{2} + 4 x + 2) d x$ $int(-2x^2+4x+2)dx$ from $[0, 3]$ $[0,3]$ ?

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Answer 1 · 2017-06-24T08:07:35

$6$ $6$

Explanation:

$integrate each term using the power rule$ $"integrate each term using the "color(blue)"power rule"$

$∙ \int a x^{n} d x = \frac{a}{n + 1} x^{n + 1}; n \neq - 1$ $• intax^ndx=a/(n+1)x^(n+1) ;n!=-1$

$\Rightarrow \int_{0}^{3} (- 2 x^{2} + 4 x + 2) d x$ $rArrint_0^3(-2x^2+4x+2)dx$

$= {[- \frac{2}{3} x^{3} + 2 x^{2} + 2 x]}_{0}^{3}$ $=[-2/3x^3+2x^2+2x]_0^3$

${[F (x)]}_{0}^{3} = F (3) - F (0)$ $[F(x)]_0^3=F(3)-F(0)$

$= (- \frac{2}{3} \times 3^{3} + 2 \times 3^{2} + 2 \times 3) - 0$ $=(-2/3xx3^3+2xx3^2+2xx3)-0$

$= 6$ $=6$

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How do you evaluate the definite integral $\int (- 2 x^{2} + 4 x + 2) d x$ $int(-2x^2+4x+2)dx$ from $[0, 3]$ $[0,3]$ ?

1 Answer

Explanation:

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How do you evaluate the definite integral ∫(−2x2+4x+2)dxint(-2x^2+4x+2)dx from [0,3][0,3]?

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How do you evaluate the definite integral $\int (- 2 x^{2} + 4 x + 2) d x$ $int(-2x^2+4x+2)dx$ from $[0, 3]$ $[0,3]$ ?