How do you evaluate the definite integral #int|x^3+64| dx# from #[-8,0]#? Calculus Introduction to Integration Formal Definition of the Definite Integral 1 Answer Cesareo R. Jul 29, 2016 #896# Explanation: #f(x) = x^3+64# changes sign for #x = -4# so #int_{-8}^0abs(f(x))dx = -int_{-8}^{-4}f(x)dx+int_{-4}^0f(x)dx# but #int_a^bf(x)dx = 64 b + b^4/4-(64 a + a^4/4)# then #int_{-8}^0 abs(f(x))dx=704 + 192 = 896# 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 1505 views around the world You can reuse this answer Creative Commons License