How do you find the definite integral of #xe^(x^2 + 2) # in the interval #[0, 2]#? Calculus Introduction to Integration Formal Definition of the Definite Integral 1 Answer Eddie Sep 7, 2016 #= e^2/2 ( e^(4) - 1)# Explanation: #int_0^2 xe^(x^2 + 2) dx = int_0^2 xe^(x^2)e^2 dx# #= e^2 int_0^2 xe^(x^2) dx# Now noting that #d/dx(e^(x^2)) = 2 x e^(x^2# #= e^2 int_0^2 d/dx (1/2 e^(x^2)) dx# and by the FTC #= e^2/2 [ e^(x^2) ]_0^2# #= e^2/2 ( e^(4) - e^0)# #= e^2/2 ( e^(4) - 1)# 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 1251 views around the world You can reuse this answer Creative Commons License