Question Type 4: Calculating the area between any function in the positive section and the x axis (using technology) Exercises

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

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

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

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

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

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

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

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

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

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

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

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