Question

The area of the region bounded by the lines x=0,x=2, and y=0 and the curve y=e^(x/2) is?

Answer 1

\[required ~area=\int\limits_{0}^{2} y~ dx=\int\limits_{0}^{2} e ^{\frac{ x }{ 2 }}dx\]
putx/2=t
x=2t
dx=2dt
when~x=0,t=0
when x=2,t=2/2=1
\[required area=2\int\limits_{0}^{1}e ^{t}~dt\]
i think now you can complete it.