Question

This question is designed to be answered with a calculator. which inequality compares the left (l), right (r), and trapezoidal (t) sum approximations of the area under the curve f(x) = 2 cos(2x) over the interval [0, pi/ 4] using 3 equal subdivisions?
a.) l < t < r
b.) r < l < t
c.) r < t < l
d.) t < r < l

Answer 1

The inequality compares the left (l), right (r), and trapezoidal (t) sum approximations of the area under the curve is C. r < t < l.

How to illustrate the inequality?

From the information given, it should be noted that f'(x) is negative. Therefore, L > R. Also since f"(x) is negative, T > R.

f(x) = 2 cos 2x.

f'(x) = -4 sin 2x

f"(x) = -8 cos 2x

Therefore, the inequality compares the left (l), right (r), and trapezoidal (t) sum approximations of the area under the curve is r < t < l

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