Math, asked by wwwmadelinechetri, 10 months ago

int 2 to 1(X² -1) dx​

Answers

Answered by Sharad001
42

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}

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