### Home > APCALC > Chapter 4 > Lesson 4.3.2 > Problem4-121

4-121.

Write each of the following integral expressions as a single integral.

1. $\int _ { 2 } ^ { 9 } ( f ( x ) ) ^ { 2 } d x - \int _ { 2 } ^ { 9 } ( g ( x ) ) ^ { 2 } d x$

$\int_{a}^{b}f(x)dx+\int_{a}^{b}g(x)dx=\int_{a}^{b}(f(x)+g(x))dx$

2. $\int _ { 3 } ^ { 5 } f ( x ) d x + \int _ { 5 } ^ { 9 } f ( x ) d x$

Translation: The area between $3$ and $5$ plus the area between $5$ and $9$.

3. $\int _ { - 2 } ^ { 1 } f ( x ) d x - \int _ { 4 } ^ { 1 } f ( x ) d x + \int _ { 4 } ^ { 9 } f ( x ) d x$

$\int_{a}^{b}f(x)dx=\int_{a}^{b}-f(x)dx$

$\int_{-2}^{9}f(x)dx$

4. $2 \int _ { 2 } ^ { 8 } k ( x ) d x + \int _ { 2 } ^ { 8 } j ( x ) d x$

Translation: TWO TIMES the area under $k\left(x\right)$ on $[2,8] +$ ONE TIME the area under $k\left(x\right)$ on $[2,8].$