Question

A. Find an expression of a(t) if delta_{t} = t/(1 + t ^ 2).
B. If A(4) = 30 find A(2).

Answer 1

Explanation:

`A (t)=\int(t)/(1+t^2) dt+c\\=(1)/(2) \int (2t)/(1+t^2) dt+c\\=(1)/(2)\ln(1+t^2)+c\\A(4)=(1)/(2)\ln(1+4^2)+c\\30=(1)/(2)\ln(17)+c\\c=30-0.5 \ln17\\A(t)=0.5\ln(1+t^2)-0.5\ln17+30\\A(2)=0.5\ln(1+2^2)-0.5 \ln17+30\\A(2)=0.5(\ln 5-\ln 17)+30\\A(2)=0.5\ln ((5)/(17) )+30`