How do you evaluate the definite integral $\int {(x - 1)}^{3} d x$ $int (x-1)^3dx$ from [2,3]?

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Answer 1 · 2018-01-16T23:53:33

$\int_{2}^{3} {(x - 1)}^{3} d x = \frac{15}{4}$ $int_2^3 (x-1)^3dx = 15/4$

$\int_{2}^{3} {(x - 1)}^{3} d x = \int_{2}^{3} {(x - 1)}^{3} d (x - 1)$ $int_2^3 (x-1)^3dx = int_2^3 (x-1)^3d(x-1)$

$\int_{2}^{3} {(x - 1)}^{3} d x = {[\frac{{(x - 1)}^{4}}{4}]}_{2}^{3}$ $int_2^3 (x-1)^3dx = [(x-1)^4/4]_2^3$

$\int_{2}^{3} {(x - 1)}^{3} d x = \frac{{(3 - 1)}^{4}}{4} - \frac{{(2 - 1)}^{4}}{4}$ $int_2^3 (x-1)^3dx = (3-1)^4/4 - (2-1)^4/4$

$\int_{2}^{3} {(x - 1)}^{3} d x = (\frac{2^{4}}{4} - \frac{1}{4})$ $int_2^3 (x-1)^3dx = (2^4/4-1/4)$

$\int_{2}^{3} {(x - 1)}^{3} d x = (\frac{16}{4} - \frac{1}{4}) = \frac{15}{4}$ $int_2^3 (x-1)^3dx = (16/4-1/4) =15/4$

How do you evaluate the definite integral ∫(x−1)3dxint (x-1)^3dx from [2,3]?