IB Mathematics Applications & Interpretation Question Type 4: Calculating the Area Between Any Function in the Positive Section and the x Axis Exercises

Using a graphing calculator, determine the area under $f(x)=e^{-x}\cos (x)$ from $x=0$ to $x=\frac{\pi }{2}$.

Calculate, using technology, the area under $f(x)=\frac{1}{x^2+1}$ above the $x$-axis from $x=0$ to $x=1$.

Using technology, find the area between $f(x)=e^x\ln (2x)$ and the $x$-axis from $x=0.5$ to $x=1$.

Find the area under $f(x)=x\ln (x)$ from $x=1$ to $x=e$ using a graphing calculator.

Calculate the area under the curve $f(x)=x^2$ above the $x$-axis between $x=0$ and $x=2$ using technology.

Using technology, compute the area under $f(x)=\ln (x+1)$ above the $x$-axis between $x=0$ and $x=2$.

Calculate the area between $f(x)=x{e}^x$ and the $x$-axis on the interval $[1,3]$ using technology.

Determine the area under the curve $f(x)=\sqrt{4-x^2}$ from $x=0$ to $x=2$ using a graphing calculator.

Determine the area under $f(x)=\sin (x^2)$ above the $x$-axis between $x=0$ and $x=\sqrt{\pi }$ using technology.

Using a graphing calculator, compute the area under $f(x)=\arctan (x)$ from $x=0$ to $x=1$.

Find the area between $f(x)=e^x$ and the $x$-axis from $x=0$ to $x=1$ using a graphing calculator.

Calculate, with technology, the area under the curve $f(x)=x{e}^{-x^2}$ above the $x$-axis between $x=0$ and $x=1$.