Use Table 5.6 to evaluate the following indefinite integrals.                                                                                                               
                                                                                                                                                                  
 (b) ∫ sec 5𝓍 tan 5𝓍 d𝓍

Displacement from a table of velocities The velocities (in mi/hr) of an automobile moving along a straight highway over a two-hour period are given in the following table.

(b) Find the midpoint Riemann sum approximation to the displacement on [0,2] with n = 2 and .n = 4 .

Working with area functions Consider the function ƒ and the points a, b, and c.

(b) Graph ƒ and A.

ƒ(𝓍) = eˣ ; a = 0 , b = ln 2 , c = ln 4

Area functions for linear functions Consider the following functions ƒ and real numbers a (see figure).

(b) Verify that A'(𝓍) = ƒ(𝓍).

ƒ(t) = 3t + 1 , a = 2

{Use of Tech} Midpoint Riemann sums with a calculator Consider the following definite integrals.

(b) Evaluate each sum using a calculator with n = 20, 50, and 100. Use these values to estimate the value of the integral.

∫₁⁴ 2√𝓍 d𝓍

{Use of Tech} Approximating net area The following functions are positive and negative on the given interval.

ƒ(x) = 4 - 2x on [0,4]

(b) Approximate the net area bounded by the graph of f and the x-axis on the interval using a left, right, and midpoint Riemann sum with n = 4.

Sigma notation Express the following sums using sigma notation. (Answers are not unique.)

(b) 4 + 5 + 6 + 7 + 8 + 9