91Ó°ÊÓ

Many computer algebra systems permit the evaluation of Riemann sums for left end point, right end point, or midpoint evaluations of the function. Using such a system, evaluate the 10 -subinterval Riemann sums using left end point, right end point, and midpoint evaluations. $$ \int_{0}^{1} \tan x d x $$

Many computer algebra systems permit the evaluation of Riemann sums for left end point, right end point, or midpoint evaluations of the function. Using such a system, evaluate the 10 -subinterval Riemann sums using left end point, right end point, and midpoint evaluations. $$ \int_{0}^{1} \cos x d x $$

use the Substitution Rule for Definite Integrals to evaluate each definite integral. $$ \int_{-1}^{3} \frac{1}{(t+2)^{2}} d t $$

Let \(x_{1}, x_{2}, \ldots, x_{n}\) be any real numbers. Find the value of \(c\) that minimizes \(\sum_{i=1}^{n}\left(x_{i}-c\right)^{2}\).

Use symmetry to help you evaluate the given integral. $$ \int_{-\pi / 2}^{\pi / 2} \frac{\sin x}{1+\cos x} d x $$

Use symmetry to help you evaluate the given integral. $$ \int_{-\sqrt[3]{\pi}}^{\sqrt[3]{\pi}} x^{2} \cos \left(x^{3}\right) d x $$

Many computer algebra systems permit the evaluation of Riemann sums for left end point, right end point, or midpoint evaluations of the function. Using such a system, evaluate the 10 -subinterval Riemann sums using left end point, right end point, and midpoint evaluations. $$ \int_{1}^{3}(1 / x) d x $$

use the Substitution Rule for Definite Integrals to evaluate each definite integral. $$ \int_{2}^{10} \frac{1}{y+4} d y $$

In the song The Twelve Days of Christmas, my true love gave me 1 gift on the first day, \(1+2\) gifts on the second day, \(1+2+3\) gifts on the third day, and so on for 12 days. (a) Find the total number of gifts given in 12 days. (b) Find a simple formula for \(T_{n}\), the total number of gifts given during a Christmas of \(n\) days.

A grocer stacks oranges in a pyramidlike pile. If the bottom layer is rectangular with 10 rows of 16 oranges and the top layer has a single row of oranges, how many oranges are in the stack?