Question

# 1. Find the area of the region bounded by the graph of the function f(x) =...

1. Find the area of the region bounded by the graph of the function f(x) = x4 − 2x2 + 8, the x-axis, and the lines x = a and x = b, where a < b and a and b are the x-coordinates of the relative maximum point and a relative minimum point of f, respectively.

2.Evaluate the definite integral.

26
2
 2x + 1
dx
0

3. Find the area of the region under the graph of f on [a, b].

f(x) = e−x/2; [−1, 14]

4. Find the area (in square units) of the region under the graph of the function f on the interval [7, 8]. f(x) = 2ex − x

5.

Find the area of the region under the graph of the function f on the interval [1, 25].

f(x) =

8
 x

6.Find the area of the region under the graph of the function f on the interval [1, 5].f(x) = 4x3

7. Find the area of the region under the graph of the function f on the interval [5, 6].

f(x) =

 2 x2

8.

Find the area of the region under the graph of the function f on the interval [0, 6].

f(x) = 6x − x2

9.

Find the area of the region under the graph of the function f on the interval [5, 7].

f(x) = 10x − 2

10.

Find the area (in square units) of the region under the graph of the function f on the interval

[1, 8],

using the Fundamental Theorem of Calculus. Then verify your result using geometry.

f(x) = −

 1 8

x + 1

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