CPM Homework Help : CALC Problem 4-110

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4-110.

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

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

$\int _ { 3 } ^ { 5 } f ( x ) d x + \int _ { 5 } ^ { 9 } f ( x ) d x$
Hint (b):
Translation: The area between $3$ and $5$ plus the area between $5$ and $9$ .

$\int _ { - 2 } ^ { 1 } f ( x ) d x - \int _ { 4 } ^ { 1 } f ( x ) d x + \int _ { 4 } ^ { 9 } f ( x ) d x$
Hint (c):
$\int_{a}^{b}f(x)dx=\int_{a}^{b}-f(x)dx$
Answer (c):
$\int_{-2}^{9}f(x)dx$

$2 \int _ { 2 } ^ { 8 } k ( x ) d x + \int _ { 2 } ^ { 8 } j ( x ) d x$
Hint (d):
Translation: TWO TIMES the area under $k(x)$ on $[2,8] +$ ONE TIME the area under $k(x)$ on $[2,8]$ .

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