Question

Cat face integrala de la 0 la 1 din sin(x+1) dx?

Answer 1

[tex]\displaystyle\limit\int\sin(x+1)dx=\\ \text{Notam:}\\ x+1=t\\ (x+1)dx=dt\\ dx=dt\\ \displaystyle\limit\int \sin t\ dt=-\cos t+C\\ \text{Deci:}\displaystyle\int \sin(x+1)\ dx=-\cos(x+1)+C\\ \text{Prin urmare:}\\ \displaystyle\int_{0}^1 \sin (x+1)\ dx=-\cos 2+\cos 1=\boxed{\cos 1-\cos 2} [/tex]