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

Find the area under the curve $f(x)=\ln(x+1)$ between $x=0$ and $x=1$.

Determine the area under $f(x)=\frac{1}{1+x^3}$ from $x=0$ to $x=2$ using technology.

Use technology to approximate the area under $f(x)=e^{-x^2}$ from $x=0$ to $x=1$.

Calculate the value of the definite integral $\int_{0}^{1}(e^x\ln(2x)-x^4)\,dx$.

Use technology to approximate the area under $f(x)=\sqrt{1+x^4}$ from $x=0$ to $x=1$.

Use technology to find the area under $f(x)=\frac{x}{x^2+1}$ from $x=0$ to $x=3$.

Calculate the exact value of the area under the curve $f(x)=x\ln(x)$ from $x=1$ to $x=2$. Verify your answer numerically.

Approximate the area under $f(x)=\sqrt{x^3+1}$ between $x=0$ and $x=2$ using a calculator.

Find the area under $f(x)=\arctan(x)$ from $x=0$ to $x=1$.