29) e^x=t e^xdx=dt
Schimbi limitele de integrare
x=0 t=e^0=1 x=1 t=e
Integrala devine
I=∫dt/(t²+1) t∈[1,e]
I=arctg t/1↑e=arctge-arctg1=arctge-π/4
30) f(x)= -x x∈[-1,0]
f)x)=x x∈[0,1]
pt x∈[-1,`1] f(x)≥g(x)
Aria=∫f(x)-g(x)]dx=∫(-x-x²)dx x∈[-1,0]+∫(x-x²)dx x∈[0,1]
x∈[-1,0] ∫(-x-x²)dx=-∫(x+x²)dx=-(x²/2-x³/3)=-(0-1/2+1/3)=-(-1/6)=1/6 (A
x∈[0,1] Aria=∫(x-x²}dx=x²/2-x³/3=1/2-1/3-0+0=1/6
Aria totala =1/6+1/6=1/3
