A function is continuous, increasing and CONCAVE UP on $\left[0,5\right]$. Put the midpoint approximation, the trapezoidal approximation and the exact integral in increasing order.

A function is continuous and DECREASING on $\left[0,2\right]$. Is a RIGHT Riemann sum an over-estimate or an under-estimate of ${\int }_0^{2}f(x)dx$?

A function is continuous and CONCAVE DOWN on $\left[0,5\right]$. Is a TRAPEZOIDAL approximation an over-estimate or an under-estimate of ${\int }_0^{5}f(x)dx$?

A function is continuous and INCREASING on $\left[0,3\right]$. Is a LEFT Riemann sum an over-estimate or an under-estimate of ${\int }_0^{3}f(x)dx$?

A function is continuous and CONCAVE DOWN on $\left[0,2\right]$. Is a MIDPOINT approximation an over-estimate or an under-estimate of ${\int }_0^{2}f(x)dx$?

A function is continuous and DECREASING on $\left[0,3\right]$. Is a LEFT Riemann sum an over-estimate or an under-estimate of ${\int }_0^{3}f(x)dx$?

A function is continuous and INCREASING on $\left[0,7\right]$. Is a RIGHT Riemann sum an over-estimate or an under-estimate of ${\int }_0^{7}f(x)dx$?

A function is continuous, decreasing and CONCAVE DOWN on $\left[0,8\right]$. Put the midpoint approximation, the trapezoidal approximation and the exact integral in increasing order.

A function is continuous and INCREASING on $\left[0,8\right]$. Put the left Riemann sum, the right Riemann sum and the exact integral in increasing order.

A trapezoidal approximation is used to estimate ${\int }_0^8(3x+2)dx$. Is it an over-estimate or an under-estimate?

A function is continuous and CONCAVE UP on $\left[0,3\right]$. Is a TRAPEZOIDAL approximation an over-estimate or an under-estimate of ${\int }_0^{3}f(x)dx$?

A function is continuous, decreasing and CONCAVE UP on $\left[0,7\right]$. Which of these approximations is an under-estimate of ${\int }_0^{7}f(x)dx$?

A function is continuous and CONCAVE UP on $\left[0,3\right]$. Is a MIDPOINT approximation an over-estimate or an under-estimate of ${\int }_0^{3}f(x)dx$?

A function is continuous, increasing and CONCAVE DOWN on $\left[0,1\right]$. Which of these approximations is an over-estimate of ${\int }_0^{1}f(x)dx$?

A function is continuous and INCREASING on $\left[0,8\right]$. With the same subintervals, its left Riemann sum is $10$ and its right Riemann sum is $14$. Which value could be ${\int }_0^{8}f(x)dx$?

A function is continuous and CONCAVE UP on $\left[0,4\right]$. With the same subintervals, its midpoint approximation is $6.2$ and its trapezoidal approximation is $6.8$. Which value could be ${\int }_0^{4}f(x)dx$?

A function is continuous and INCREASING on $\left[0,1\right]$. A left Riemann sum is redone with twice as many subintervals. Is the new sum an over-estimate or an under-estimate of ${\int }_0^{1}f(x)dx$?

A function is continuous, NEGATIVE and INCREASING on $\left[0,2\right]$. Is a RIGHT Riemann sum an over-estimate or an under-estimate of ${\int }_0^{2}f(x)dx$?

On $\left[0,7\right]$, a function has $f^{\prime }(x)<0$ and $f^{\prime \prime }(x)<0$. Is a LEFT Riemann sum an over-estimate or an under-estimate of ${\int }_0^{7}f(x)dx$?

A function is continuous and DECREASING on $\left[0,1\right]$. Put the left Riemann sum, the right Riemann sum and the exact integral in increasing order.