Question

Solve this,,,,,

1) ∫x³.dx

2) ∫x⁹.dx

3) ∫x².dx

​

Answer 1

1)

$\int {x}^{3} dx$

$= > \frac{ {x}^{3 + 1} }{3 + 1} + c$

$= > \frac{ {x}^{4} }{4}$

2)

$\int {x}^{9} .dx$

$= > \frac{ {x}^{9 + 1} }{9 + 1} + c$

$= > \frac{ {x}^{10} }{10}$

3)

$\int \: {x}^{2} .dx$

$= > \frac{ {x}^{2 + 1} }{2 + 1}$

$= > \frac{ {x}^{3} }{3}$

Answer 2

Explanation :

According to the power rule,

$\bold \red{ \int x {}^{n} .dx} \: \rightarrow \bold \green{ \dfrac{x {}^{n + 1} }{n + 1} + c}$

Case (I), ㅤ$\sf \int x {}^{3} .dx$

$\mapsto \sf \: \dfrac{x {}^{3 + 1} }{3 + 1} + c$

$\mapsto { \boxed{ \sf{\dfrac{x {}^{4} }{4} + c}}} \: \bigstar$

ㅤㅤㅤㅤㅤ

Case (II), ㅤ$\sf \int x {}^{9} .dx$

$\mapsto \sf \: \dfrac{x {}^{9 + 1} }{9 + 1} + c$

$\mapsto{ \boxed{ \sf{ \frac{x {}^{10} }{10} + c}}} \: \bigstar$

ㅤㅤㅤㅤㅤ

Case (III), ㅤ $\sf\int x {}^{2} .dx$

$\mapsto \sf \: \dfrac{x {}^{2 + 1} }{2 + 1} + c$

$\mapsto{ \boxed{ \sf{ \frac{x {}^{3} }{3} + c}}} \: \bigstar$

_____________________