Let f(x)= 4-3x. Find K so that the integral from -1 to x of f(t)dt+k = the integral from 3 to x of f(t)?Also find d/dx the integral from -1 to x...

justinbains132,

the intergral from -1 to x of f(t)dt+k is

(-3/2)*x^2 + (4 + k)*x + 11/2 + k

the integral from 3 to x of f(t) is

(-3/2)*x^2 + 4x + 3/2

These two values are equal, so

(-3/2)*x^2 + (4 + k)*x + 11/2 + k = (-3/2)*x^2 + 4x + 3/2

If we simplify this equation,

k*x = -k - 4

If we solve this equation to k,

k = 4/(x+1)

d/dx the integral from -1 to x of f(t)dt is

4 -  3x