91Ó°ÊÓ

In Exercises \(19-30,\) evaluate the integral using antiderivatives, as in Example \(4 .\) $$\int _ { 1 } ^ { e } \frac { 1 } { x } d x$$

In Exercises \(27-40\) , evaluate each integral using Part 2 of the Fundamental Theorem. Support your answer with NINT if you are unsure. $$\int_{2}^{-1} 3^{x} d x$$

In Exercises \(27-40\) , evaluate each integral using Part 2 of the Fundamental Theorem. Support your answer with NINT if you are unsure. $$\int_{0}^{1}\left(x^{2}+\sqrt{x}\right) d x$$

In Exercises \(29-32,\) express the desired quantity as a definite integral and evaluate the integral using Theorem \(2 .\) Find the distance traveled by a train moving at 87 mph from \(8 : 00\) A.M. to \(11 : 00\) A.M.

In Exercises \(19-30,\) evaluate the integral using antiderivatives, as in Example \(4 .\) $$\int _ { 1 } ^ { e } \frac { 1 } { x } d x$$

In Exercises \(19-30,\) evaluate the integral using antiderivatives, as in Example \(4 .\) $$\int _ { 1 } ^ { 4 } - x ^ { - 2 } d x$$

In Exercises \(27-40\) , evaluate each integral using Part 2 of the Fundamental Theorem. Support your answer with NINT if you are unsure. \(\int_{0}^{5} x^{3 / 2} d x\)

In Exercises \(31 - 36 ,\) find the average value of the function on the interval, using antiderivatives to compute the integral. $$y = \sin x , \quad [ 0 , \pi ]$$

True or False The Trapezoidal Rule will underestimate \(\int_{a}^{b} f(x) d x\) if the graph of \(f\) is concave up on \([a, b] .\) Justify your answer.

In Exercises \(27-40\) , evaluate each integral using Part 2 of the Fundamental Theorem. Support your answer with NINT if you are unsure. $$\int_{1}^{32} x^{-6 / 5} d x$$