Question

int 2 to 1(X² -1) dx​

Answer 1

Question :-

integrate it

$\red{ \int\limits_{2}^{1} } \green{\sf{ {(x}^{2} - 1)}}dx$

Answer :-

$\\ \rightarrow \: \red{ \int\limits_{2}^{1} } \green{\sf{ {(x}^{2} - 1)}}dx = \frac{ - 10}{3} \:$

Used formula :-

$\sf{defefinite \: intgrals \: }\\ \star \sf{ \int {x}^{n}dx = \frac{ {x}^{n + 1} }{n + 1} } \\ \\ \star \: \int \: 1 \sf dx = x \:$

Explanation :-

We have ,

$\implies \: \red{ \int\limits_{2}^{1} } \green{\sf{ {(x}^{2} - 1)}}dx \\ \: \\ \implies \sf{ \frac{ {x}^{3} }{3} + x} \\ \sf{taking \: limits} \\ \\ \rightarrow \: \frac{1}{3} + 1 - \frac{8}{3} - 2 \\ \\ \rightarrow \: \frac{1 + 3 - 8 - 6}{3} \\ \\ \rightarrow \: \frac{ - 10}{3} \\ \\ \rightarrow \: \red{ \int\limits_{2}^{1} } \green{\sf{ {(x}^{2} - 1)}}dx = \frac{ - 10}{3}$