Answer to Question #5232 in Calculus for Jessica

Question

Find the antiderivative F of f that satisfies the given condition. Check your answer by comparing the graphs of f and F. f(x)=4-3*(1+x^2)^-1, F(1)=0

Answer 1

<img src="../../..//assignments/uploaded_files/static/25/dc/25dcee4d26842f0f6c1c1603b859ed8e.png" title="" alt="">
F(1)=0=4-3/tan(1)+C
C=3/tan(1)-4
F(x)=4x-3/tan(x)+3/tan(1)-4