Math, asked by 20ece051, 4 months ago

integral 1 to 2x²(1-x)³ dx​

Answers

Answered by senboni123456
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}   \\

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