Question Type 4: Calculating the area between any function in the positive section and the x axis (using technology) 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 $x=1$.