How do you use a Power Series to estimate the integral #int_0^0.01e^(x^2)dx# ? Calculus Power Series Power Series and Estimation of Integrals 1 Answer Wataru Oct 16, 2014 Since #e^x=1+x+x^2/{2!}+cdots#, #e^{x^2}=1+x^2+x^4/{2!}+cdots# #int_0^{0.01}e^{x^2}dx=int_0^{0.01} (1+x^2+x^4/{2!}+cdots)dx# #=[x+x^3/3+x^5/{10}+cdots]_0^{0.01}# #=0.01+(0.01)^3/3+(0.01)^5/10+cdots# #approx 0.01# I hope that this was helpful. Answer link Related questions How do you use a Power Series to estimate an integral? How do you use a Power Series to estimate the integral #int_0^0.01cos(x^2)dx# ? How do you use a Power Series to estimate the integral #int_0^0.01sin(x^2)dx# ? How do you use a Power Series to estimate the integral #int_0^0.01cos(sqrt(x))dx# ? How do you use a Power Series to estimate the integral #int_0^0.01sin(sqrt(x))dx# ? What is the integral of #ln (x)/x^2#? See all questions in Power Series and Estimation of Integrals Impact of this question 2242 views around the world You can reuse this answer Creative Commons License