Thread: Fundamental Theorum of Integral

Find f and a that

Originally Posted by camherokid

Find f and a that

6 + integal_{t=a to x} f(t)/t^2 dt = 2 sqrt(x)

1. When x=a the integral is zero, so:

6 = 2 sqrt(a),

or a = 9.

2. Differentiate (by the FTC d/dx[integal_{t=a to x} f(t)/t^2 dt] = f(x)/x^2)

f(x)/x^2 = 1/sqrt(x)

so: f(x) = x^{3/2}.

RonL