Let $f$ be continuous and decreasing on $[0,3]$. If $L$ is a left Riemann sum and $R$ is a right Riemann sum for $\int_0^3 f(x)\,dx$ with equal subintervals, which of the following must be true?

Question

Accepted Answer

A. $L>\int_0^3 f(x)\,dx>R$

Answer

$L>\int_0^3 f(x)\,dx>R$

Answer

$R>\int_0^3 f(x)\,dx>L$

Answer

$L=\int_0^3 f(x)\,dx=R$

Answer

$L<\int_0^3 f(x)\,dx<R$

Let $f$ be continuous and decreasing on $[0,3]$ . If $L$ is a left Riemann sum and $R$ is a right Riemann sum for $\int_0^3 f(x)\,dx$ with equal subintervals, which of the following must be true?

Explanation

Core Concept

Correct Answer

More Unit 6: Integration and Accumulation of Change practice questions

Let fff be continuous and decreasing on [0,3][0,3][0,3]. If LLL is a left Riemann sum and RRR is a right Riemann sum for ∫03f(x) dx\int_0^3 f(x)\,dx∫03​f(x)dx with equal subintervals, which of the following must be true?

Explanation

Core Concept

Correct Answer

More Unit 6: Integration and Accumulation of Change practice questions

Let $f$ be continuous and decreasing on $[0,3]$ . If $L$ is a left Riemann sum and $R$ is a right Riemann sum for $\int_0^3 f(x)\,dx$ with equal subintervals, which of the following must be true?