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[tex]\int_{1}^{2}\frac{\sqrt{e^{-x^{2}}}}{x^{2}} dx \\[/tex]

[tex]a=1\\[/tex]

[tex]b=2 \\[/tex]

[tex]n=8\\[/tex]

[tex]\Delta x=\frac{b-a}{n}=\frac{2-1}{8}=\frac{1}{8}\\[/tex]

[tex]x_{0}= 1 \\[/tex]

[tex]x_{1}= x_{0}+\Delta x=1+\frac{1}{8}= \frac{9}{8}\\[/tex]

[tex]x_{2}= x_{1}+\Delta x=\frac{9}{8}+\frac{1}{8}= \frac{5}{4}\\[/tex]

[tex]x_{3}= x_{2}+\Delta x=\frac{5}{4}+\frac{1}{8}= \frac{11}{8}\\[/tex]

[tex]x_{4}= x_{3}+\Delta x=\frac{11}{8}+\frac{1}{8}= \frac{6}{4}\\[/tex]

[tex]x_{5}= x_{4}+\Delta x=\frac{6}{4}+\frac{1}{8}= \frac{13}{8}\\[/tex]

[tex]x_{6}= x_{5}+\Delta x=\frac{13}{8}+\frac{1}{8}= \frac{7}{4}\\[/tex]

[tex]x_{7}= x_{6}+\Delta x=\frac{7}{4}+\frac{1}{8}= \frac{15}{8}\\[/tex]

[tex]x_{8}= x_{7}+\Delta x=\frac{15}{8}+\frac{1}{8}= 2\\[/tex]

[tex]\frac{\sqrt{e^{-\1^{2}}}}{\1^{2}} dx =0,6065\\[/tex]

[tex]\frac{\sqrt{e^{-\frac{9}{8}^{2}}}}{\frac{9}{8}^{2}} dx =0,4196\\[/tex]

[tex]\frac{\sqrt{e^{-\frac{5}{4}^{2}}}}{\frac{5}{4}^{2}} dx =0,293\\[/tex]

[tex]\frac{\sqrt{e^{-\frac{11}{8}^{2}}}}{\frac{11}{8}^{2}} dx =0,08\\[/tex]

[tex]\frac{\sqrt{e^{-\frac{6}{4}^{2}}}}{\frac{6}{4}^{2}} dx =0,144\\[/tex]

[tex]\frac{\sqrt{e^{-\frac{13}{8}^{2}}}}{\frac{13}{8}^{2}} dx =0,1011\\[/tex]

[tex]\frac{\sqrt{e^{-\frac{7}{4}^{2}}}}{\frac{7}{4}^{2}} dx =0,071\\[/tex]

[tex]\frac{\sqrt{e^{-\frac{15}{8}^{2}}}}{\frac{15}{8}^{2}} dx =0,05\\[/tex]

[tex]\frac{\sqrt{e^{-\2^{2}}}}{\2^{2}} dx =0,033\\[/tex]

[tex]\int_{1}^{2}\frac{\sqrt{e^{-x^{2}}}}{x^{2}} dx  =\frac{b-a}{3n}\left \{  f\left (x _{0} \right )+4f\left ( x_{1} \right )+2f\left ( x_{2} \right )+4f\left ( x_{3} \right )+2f\left ( x_{4} \right )+4f\left ( x_{5} \right )+2f\left ( x_{6} \right )+4f\left ( x_{7}\right)+f\left (x _{8} \right ) \right \}\\ [/tex]

[tex]\int_{1}^{2}\frac{\sqrt{e^{-x^{2}}}}{x^{2}} dx  =\frac{2-1}{3\left ( 8 \right )}\left \{  f\left (x _{0} \right )+4f\left ( x_{1} \right )+2f\left ( x_{2} \right )+4f\left ( x_{3} \right )+2f\left ( x_{4} \right )+4f\left ( x_{5} \right )+2f\left ( x_{6} \right )+4f\left ( x_{7}\right)+f\left (x _{8} \right ) \right \}\\ [/tex]

[tex]\int_{1}^{2}\frac{\sqrt{e^{-x^{2}}}}{x^{2}} dx  =\frac{1}{24}\left \{  f\left (x _{0} \right )+4f\left ( x_{1} \right )+2f\left ( x_{2} \right )+4f\left ( x_{3} \right )+2f\left ( x_{4} \right )+4f\left ( x_{5} \right )+2f\left ( x_{6} \right )+4f\left ( x_{7}\right)+f\left (x _{8} \right ) \right \}\\ [/tex]

[tex]\int_{1}^{2}\frac{\sqrt{e^{-x^{2}}}}{x^{2}} dx  =\frac{1}{24}\left \{  f\left (1\right )+4f\left ( 1,125\right )+2f\left ( 1,25 \right )+4f\left ( 1,375 \right )+2f\left ( 1,5 \right )+4f\left ( 1,625 \right )+2f\left ( 1,75 \right )+4f\left ( 1,875\right)+f\left (2 \right ) \right \}\\ [/tex]

[tex]\int_{1}^{2}\frac{\sqrt{e^{-x^{2}}}}{x^{2}} dx  =\frac{1}{24}\left \{ 0,60653  \right )+4( 0,4196\right )+2 ( 0,293\right )+4 (0,08\right )+2(0,144 \right )+4 ( 0,101\right )+2(0,071\right )+4 ( 0,05\right)+ (0,033 \right ) \right \}\\ [/tex]

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