Question

高数定积分题一枚,证明,当x→∞时,∫［0,x］e∧（x∧2）dx～1/（2x）e∧（x∧2）.

Answer 1

∫e^(x^2)dx=(1/2)∫e^x^2dx^2/x

=(1/2)∫d(e^x^2)/x

=(1/2)e^(x^2)/x -(1/4)e^(x^2)/x^3+...+(-1)^(n-1)/(2^n)e^x^2/x^(2n-1)

x→∞,∫[0,x]e^x^2dx ≈(1/2)e^(x^2)/x