How do you find the antiderivative of #f(x)=4x^2-6x+7#? Calculus Introduction to Integration Formal Definition of the Definite Integral 1 Answer Alan N. Mar 7, 2017 #int f(x) dx = 4/3x^3-3x^2+7x+C# Explanation: #f(x) = 4x^2-6x+7# #int f(x) dx = int (4x^2-6x+7)dx# #= 4*int x^2 dx -6* int xdx+7* int 1dx# Applying the power rule to each term: #= (4x^3)/3 - (6x^2)/2 +(7x^1)/1 +C# #= 4/3x^3-3x^2+7x+C# 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 3543 views around the world You can reuse this answer Creative Commons License