Let be a positive

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Let

f

be a positive, decreasing function on the interval

[2,6]

. When equal subintervals are used, which of the following correctly compares the left and right Riemann sums,

L_{n}

and

R_{n}

, to

\displaystyle\int_{2}^{6}f(x)\,dx

? (a)

L_{n}

is less than the integral, and

R_{n}

is greater than the integral. (b) Both

L_{n}

and

R_{n}

are less than the integral. (c)

L_{n}

is greater than the integral, and

R_{n}

is less than the integral. (d) Both

L_{n}

and

R_{n}

are greater than the integral.