Calculate The Value For The Following Improper Integral
Answer : Question 1: your way is not correct (reason: see my answer to question 2). Question 2: ∫ 0 ∞ \int_0^{\infty} ∫ 0 ∞ is convergent ⟺ \iff ⟺ the integrals ∫ 0 1 , ∫ 1 3 / 2 \int_0^{1},\int_{1}^{3/2} ∫ 0 1 , ∫ 1 3/2 and ∫ 3 / 2 ∞ \int_{3/2}^{\infty} ∫ 3/2 ∞ are all convergent. Now show that ∫ 0 1 d x 2 x 2 − 5 x + 3 \int_0^{1}\frac{dx}{2x^2-5x+3} ∫ 0 1 2 x 2 − 5 x + 3 d x is divergent ! Conclusion: ∫ 0 ∞ d x 2 x 2 − 5 x + 3 \int_0^{\infty}\frac{dx}{2x^2-5x+3} ∫ 0 ∞ 2 x 2 − 5 x + 3 d x is divergent.