What is the integral of #|x|#? Calculus Introduction to Integration Integrals of Polynomial functions 1 Answer YouDid Dec 17, 2014 Let's take #a<0# and #b>0#, then #int_a^b |x|dx = int_a^0-xdx + int_0^bxdx = int_0^-axdx + int_0^bxdx = [1/2x^2]_0^-a +[1/2x^2]_0^b= 1/2(-a)^2+1/2b^2 = 1/2a^2+1/2b^2# Answer link Related questions How do you evaluate the integral #intx^3+4x^2+5 dx#? How do you evaluate the integral #int(1+x)^2 dx#? How do you evaluate the integral #int8x+3 dx#? How do you evaluate the integral #intx^10-6x^5+2x^3 dx#? What is the integral of a constant? What is the antiderivative of the distance function? What is the integral of #3x#? What is the integral of #4x^3#? What is the integral of #sqrt(1-x^2)#? What is the integral of #sqrt(9-x^2)#? See all questions in Integrals of Polynomial functions Impact of this question 5575 views around the world You can reuse this answer Creative Commons License