IB Mathematics Applications & Interpretation Question Type 2: Calculating the Area Between a Function and the X-axis Exercises

Calculate the area of the region bounded by the curve $y=e^{x/2}$, the $y$-axis, and the horizontal lines $y=2$ and $y=e^2$.

Calculate the exact value of the definite integral ${\int }_1^4(x^2-5x)dx$ and state its geometric interpretation.

Find the area enclosed by the $y$-axis and the curve $y={\text{e}}^{x/2}$ for $1\le y\le \text{e}$.

Calculate the net signed area between the $x$-axis and the curve $y=x^2-5x$ from $x=0$ to $x=7$.

A region is bounded by the curve $y=e^{x/2}$, the $x$-axis, the $y$-axis, and the line $x=2$. Find its exact area.

Calculate the area enclosed by the $x$-axis and the curve $y=x^2-5x$ between its $x$-intercepts.

Find the area enclosed by the curve $y=e^{x/2}$, the $y$-axis, and the line $y=4$.

Find the area of the region enclosed by the curve $y=e^{x/2}$ and the lines $y=4$, $x=0$, and $x=1$.

Find the area enclosed by the curve $y=x^2-5x$, the lines $x=2.5$, $x=7.5$, and the $x$-axis.

Find the area of the region bounded by the curve $y=e^{x/2}$, the $x$-axis, the $y$-axis, and the vertical line $x=4$.

Calculate the total area between the $x$-axis and the curve $y=x^2-5x$ on the interval $[-1,6]$.