Are the following statements true or false? Choose True if the statement is always true, and otherwise choose False.

b b ? 6. If f is continuous on the interval [a, b], then xf(x) dx = x f(x) dx. a a ? 7. Integrals can be used to derive or come up with some familiar geometry formulas, such as the area of a trapezoid. ? 8. (Challenge) Riemann sums are somewhat cumbersome tools for finding approximations of areas, yet they are absolutely necessary to link antiderivatives to areas. 5 ? 9. To calculate the definite integral 25 - x2 dx, we must find an antiderivative of \\ 25 - x2 and 5 evaluate it at the ends of the interval [-5, 5]. ? 10. When asked for the area of a region, it's fine to give a negative answer if it is bounded above by the x -axis and below by some function f (x)