How do you find the definite integral of 2 / (4+x^2) dx from [0, 2]? Calculus Introduction to Integration Formal Definition of the Definite Integral 1 Answer G_Dub Apr 8, 2018 pi/4 Explanation: The integral of a/(a^2+x^2) with respect to x is tan^(-1)(x/a) therefore the integral of2/(4+x^2)=tan^(-1)(x/2) where a=2 So, int_0^2 2/(4+x^2) dx =[tan^(-1)(x/2)]_0^2 =tan^(-1)1-tan^(-1)0 =pi/4-0 =pi/4 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 1594 views around the world You can reuse this answer Creative Commons License