Question

integral 1 to 2x²(1-x)³ dx​

Answer 1

Step-by-step explanation:

We have,

$\int \limits^{2}_{1} {x}^{2} (1 - x)^{3} dx$

$= \int \limits^{2}_{1} {x}^{2} (1 - x^{3} - 3x + 3 {x}^{2} ) dx$

$= \int \limits^{2}_{1} ({x}^{2} - x^{5} - 3x ^{3} + 3 {x}^{4} ) dx$

$= [ \frac{{x}^{3} }{3} - \frac{ x^{6} }{6}- \frac{ 3x ^{4}}{4} + \frac{3 {x}^{5}}{5}] ^{2}_{1}$

$= \frac{8}{3} - \frac{64}{6} - \frac{48}{4} + \frac{96}{5} - \frac{1}{3} + \frac{1}{ 6} + \frac{1}{4} - \frac{1}{5}$

$= \frac{7}{3} - \frac{63}{6} - \frac{47}{4} + \frac{95}{5}$