Math
Definite Integrals Solutions
7.
X
R
Let R be the shaded region bounded by the graph fy = xex?, the line y=2x, and the vertical line x = 1 as
shown in the figure above.
=
(a) Find the area of R.
(b) Write, but do not evaluate, an integral expression that gives the volume of the solid generated when R is
rotated about the horizontal line y=2
(c) Region R is the base of a solid. For this solid, each cross section perpendicular
right triangle with a leg in R. Find the volume of the solid.
the xaxis is an isosceles
For #8  18, choose the correct answer and write it on the provided line.

8. Let f be the function give by f(x) = 300x  x? On which of the following intervals
is the function f increasing?
C) (10,10]
A) (0, 10] and [10, 0)
D) (0, 10/3] only
B) (0, 10) only
E) (0,00)
9. What is the area of the region in the first quadrant bounded by the graph of y =
and the line x = 2?
A) 2e  2
B) 2e

1
el
E) e  1
2
10. If f(x) = 7x – 3 + ln x, then f'(1) =
A) 4
B) 5
C) 6
D) 7
E) 8