Question

f(x)este egal cu x+arctgx.val integralei de la 0 la 1+pi/4 din f la -1

Answer 1

Răspuns:

Explicație pas cu pas:

$\displaystyle\int_0^{1+\frac{\pi}{4}} f^{-1}(x) dx=\int_0^{1}f'(t)dt=f(t)|_0^1=f(1)-f(0)=\boxed{1+\dfrac{\pi}{4}}\\f^{-1}(x)=t\\x=f(t)\\dx=f'(t)dt$