Question Type 1: Area enclosed by the y-axis and a function Bootcamps

Find the area enclosed by the y-axis, the curve $y = \frac{e^x}{2}$, and the lines $x=0$ and $x=1$.

Calculate the area bounded by the y-axis, the curve $y = \frac{e^x}{2}$, and the vertical lines $x=0$ and $x=2$.

Determine the area under the curve $y=\frac{e^x}{2}$ between $x=-1$ and the y-axis.

Find the area enclosed by the y-axis, the curve $y=\frac{e^x}{2}$, and the lines $x=1$ and $x=3$.

Determine the value of $k$ such that the area of the region bounded by the y-axis, the curve $y=\frac{e^x}{2}$, and the horizontal line $y=k$ is 1.

Find the value of $a$ such that the area under $y=\frac{e^x}{2}$ from $x=0$ to $x=a$ equals 1.

An engineer requires the cumulative area under $y=\frac{e^x}{2}$ from $x=0$ to $x=L$ to be at least 5. Find the minimal $L$.

Find the average value of $y=\frac{e^x}{2}$ on the interval $[0,2]$.

Determine $b>0$ such that the average value of $y=\frac{e^x}{2}$ on $[0,b]$ is 1.

Find the area of the region bounded by the y-axis and the inverse of the curve $y=\tfrac{e^x}{2}$ between $y=1$ and $y=2$.