06.04 Applying Properties of Definite Integrals

If integral from 0 to 4 of f of x times d times x equals 8 and integral from 4 to 6 of f of x times d times x equals 3, then what is integral from 0 to 6 of f of x times d times x?

11

Consider the function g that is continuous on the interval [−10, 10] and for which integral from 0 to 10 of g of x times d times x equals 8. What is integral from 0 to 10 of open bracket g of x plus 2 close bracket times d times x equal to?

28

The graph of the function f on the interval 0 ≤ x ≤ 6 consists of a line segment and a semicircle, as shown in the figure. What is the value of integral from 0 to 6 of the function f of x times d times x? graph of line segment decreasing from (0,3) to (2,0) and a semicircle from (2,0) to (4,-2) to (6,0).

3 − 2π

If f of x is equal to the quantity x plus 1 end quantity times the quantity x minus 2 end quantity divided by the absolute value of the quantity x minus 2 end quantity, then the value of integral from 0 to 4 of f of x times d times x is equal to which value?

4

The graph of the piecewise function g is composed of three line segments on the interval −4 ≤ x ≤ 4. What is integral from negative 4 to 4 of g of x times d times x? graph of horizontal line segment from (-4,3) to (-1,3) and then a decreasing line segment to (2,-3) and then an increasing line segment to (4,-1).

5