Menu Close

1-1-3-3-1-5-5-1-7-7-




Question Number 124892 by Dwaipayan Shikari last updated on 06/Dec/20
1−(1/(3.3!))+(1/(5.5!))−(1/(7.7!))+...
$$\mathrm{1}−\frac{\mathrm{1}}{\mathrm{3}.\mathrm{3}!}+\frac{\mathrm{1}}{\mathrm{5}.\mathrm{5}!}−\frac{\mathrm{1}}{\mathrm{7}.\mathrm{7}!}+… \\ $$
Commented by Dwaipayan Shikari last updated on 06/Dec/20
∫_0 ^1 ((sinx)/x)dx=∫_0 ^1 1−(x^2 /(3!))+(x^4 /(5!))−(x^6 /(7!))+...                    = 1−(1/(3.3!))+(1/(5.5!))−(1/(7.7!))+....  ∫_0 ^1 ((sinx)/x)dx=Si(1)=0.94
$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{sinx}}{{x}}{dx}=\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{1}−\frac{{x}^{\mathrm{2}} }{\mathrm{3}!}+\frac{{x}^{\mathrm{4}} }{\mathrm{5}!}−\frac{{x}^{\mathrm{6}} }{\mathrm{7}!}+… \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\mathrm{1}−\frac{\mathrm{1}}{\mathrm{3}.\mathrm{3}!}+\frac{\mathrm{1}}{\mathrm{5}.\mathrm{5}!}−\frac{\mathrm{1}}{\mathrm{7}.\mathrm{7}!}+…. \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{sinx}}{{x}}{dx}={Si}\left(\mathrm{1}\right)=\mathrm{0}.\mathrm{94} \\ $$
Commented by mnjuly1970 last updated on 06/Dec/20
nice  si(x)=∫_0 ^( x) ((sin(t))/t)dt
$${nice} \\ $$$${si}\left({x}\right)=\int_{\mathrm{0}} ^{\:{x}} \frac{{sin}\left({t}\right)}{{t}}{dt} \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *