Homework Soursegiven the function fx2x3x2 3x12 Use the fundamental theorem
given the function: f(x)=(2x+3)(x^2 + 3x+1)^2
Use the fundamental theorem of calculus to find the definite integral of f(x) as x varies from 2 to 5.
Use the fundamental theorem of calculus to find the definite integral of f(x) as x varies from 2 to 5.
Solution
let (x^2 + 3x+1) = t (2x+3) dx = dt integral (2x+3) (x^2 + 3x+1)^2 dx => integral t^2 dt = t^3/3 for x (2 to5) = (1/3) (x^2 + 3x+1)^3 for x (2 to5) => (1/3) ( 41-11) =10
