Let $f$ be continuous with $f''(x)0$ on $[0,2]$. If $T$ is the trapezoidal approximation of $\int_0^2 f(x)\,dx$ with equal subintervals, which of the following must be true?

Question

Let $f$ be continuous with $f''(x)>0$ on $[0,2]$. If $T$ is the trapezoidal approximation of $\int_0^2 f(x)\,dx$ with equal subintervals, which of the following must be true?

Accepted Answer

A. $T>\int_0^2 f(x)\,dx$

Answer

$T>\int_0^2 f(x)\,dx$

Answer

$T<\int_0^2 f(x)\,dx$

Answer

$T=\int_0^2 f(x)\,dx$

Answer

It cannot be determined

Let $f$ be continuous with $f''(x)>0$ on $[0,2]$ . If $T$ is the trapezoidal approximation of $\int_0^2 f(x)\,dx$ 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 with f′′(x)>0f''(x)>0f′′(x)>0 on [0,2][0,2][0,2]. If TTT is the trapezoidal approximation of ∫02f(x) dx\int_0^2 f(x)\,dx∫02​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 with $f''(x)>0$ on $[0,2]$ . If $T$ is the trapezoidal approximation of $\int_0^2 f(x)\,dx$ with equal subintervals, which of the following must be true?