Question

For (x^2)(e^(x^2)) finf the power series representation using previously known power series e^x . Also find the approximate value of the integral from 0 to 1 of (x^2)(e^(x^2)) with 4 terms

Answer 1

As we know series for e^x as:

So we can write it in summation form as:

If we replace x from x^2

  

Sow e can approx integral by four term as: