Question

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) = 2e^x − 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

Answer 1