Question

If m ≤ f(x) ≤ M for a ≤ x ≤ b, where m is the absolute minimum and M is the absolute maximum of f on the interval [a, b], then

Answer 1

\[m(b-a) \le \int\limits_{a}^{b} f(x) dx \le M(b-a)\]

Answer 2

Estimate the smallest and largest value for
\[\int\limits_{5\pi}^{6\pi} (5x - 10sinx) dx\]

Answer 3

f(x)=(5/2 (x^2+4 cos(x))
you just need to substitute the 6pi in to x and 5pi, then do f(6pi)-f(5pi)

Answer 4

but wouldn't subtracting 6pi and 5pi give u the area?

Answer 5

how do you determine the max and min?