How do you find the definite integral of #x * e^ (-x^2) dx# from #[1, sqrt2]#? Calculus Introduction to Integration Formal Definition of the Definite Integral 1 Answer Cem Sentin Feb 20, 2018 #1/2*(e^(-1)-e^(-2))# Explanation: #int_1^sqrt2 xe^(-x^2)*dx# =#-1/2int_1^sqrt2 -2xe^(-x^2)*dx# =#[-1/2e^(-x^2)]_1^sqrt2# =#1/2*(e^(-1)-e^(-2))# Answer link Related questions What is the Formal Definition of the Definite Integral of the function #y=f(x)# over the... How do you use the definition of the definite integral? What is the integral of dy/dx? What is an improper integral? How do you calculate the double integral of #(xcos(x+y))dr# where r is the region: 0 less than... How do you apply the evaluation theorem to evaluate the integral #3t dt# over the interval [0,3]? What is the difference between an antiderivative and an integral? How do you integrate #3x^2-5x+9# from 0 to 7? Question #f27d5 How do you evaluate the definite integral #int sqrtt ln(t)dt# from 2 to 1? See all questions in Formal Definition of the Definite Integral Impact of this question 1453 views around the world You can reuse this answer Creative Commons License