Practice section 2 of 9

Evaluate $\int_0^2 3(1+x^2)\,dx$.

Evaluate $\int_0^4\frac2{2+\sqrt x}\,dx$.

Find the area of the region bounded by $y=x^2-6x+8$, the $x$-axis and the lines $x=1$ and $x=5$.

Find the exact area of the region bounded by $y=\frac{x}{x+3}$, the $x$-axis, and the lines $x=-1$ and $x=2$.

Without using a calculator, find the area of the region bounded by $f(x)=|x^2-4|$, the $x$-axis and the lines $x=0$ and $x=3$.

Without using a calculator, identify which of the following definite integral(s) has a different value. Refer to the sketch from Example 9: (a) $\int_{-2}^0|x^2-4|\,dx$, (b) $\int_{-2}^0(x^2-4)\,dx$, (c) $-\int_{-2}^0(x^2-4)\,dx$. You can check your own answer using the graphing calculator.