Integration Questions

Question Number 56061 by necx1 last updated on 09/Mar/19

$$\int_{\mathrm{0}} ^{\mathrm{1}} {e}^{−{x}^{\mathrm{2}} } {dx}\:{correct}\:{to}\:\mathrm{3}\:{decimal}\:{place}. \\$$

Answered by tanmay.chaudhury50@gmail.com last updated on 09/Mar/19

$$\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}−{x}^{\mathrm{2}} +\frac{{x}^{\mathrm{4}} }{\mathrm{2}!}−\frac{{x}^{\mathrm{6}} }{\mathrm{3}!}+\frac{{x}^{\mathrm{8}} }{\mathrm{4}!}−...\right){dx} \\$$ $$\mid{x}−\frac{{x}^{\mathrm{3}} }{\mathrm{3}}+\frac{{x}^{\mathrm{5}} }{\mathrm{10}}−\frac{{x}^{\mathrm{7}} }{\mathrm{42}}+\frac{{x}^{\mathrm{9}} }{\mathrm{216}}\mid_{\mathrm{0}} ^{\mathrm{1}} \\$$ $$=\frac{\mathrm{1}}{\mathrm{1}}−\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{10}}−\frac{\mathrm{1}}{\mathrm{42}}+\frac{\mathrm{1}}{\mathrm{216}} \\$$ $$=\mathrm{1}+\mathrm{0}.\mathrm{1}+\mathrm{0}.\mathrm{0046}−\mathrm{0}.\mathrm{33}−\mathrm{0}.\mathrm{0238} \\$$ $$\mathrm{1}.\mathrm{1046}−\mathrm{0}.\mathrm{3538} \\$$ $$\approx>.\mathrm{7508} \\$$

Commented bytanmay.chaudhury50@gmail.com last updated on 09/Mar/19

Commented bynecx1 last updated on 09/Mar/19

$${thank}\:{you}\:{so}\:{much}. \\$$