Review - Definite Integrals (end of Chapter 5)

Calculus Review Worksheet
(1) Evaluate each of the following integrals please.
2
4 2
(a) ( )
∫
x + 4x dx
(e)
0
2
e
∫
e
dx
x ln x
( )
(b)
∫
2
3x dx
0 3 2
7x
−1
(f)
∫
3
4
1
2
dx
x 1
−
x
π
∫
2
(c) sin ( x) cos( x)dx
− π
4
3
(g)
π
∫
2
−
π
2
( )
cos x dx
2
( )
1 + sin x
π
8
∫
2
(d) tan ( 2x)dx
− π
8
(h)
∫
2
0
2 2
x 4 − x dx
(2) Find the area under the graph of
x = 0 and x = 2.
y = x
2
3x + 4 and above the x-axis, between
(3) Find the area under one arch of the graph of y = cos( x)
3 π and above the x-axis.
3 2
(4) Find the total area bound by the x-axis and the graph of y = x + 5x + 6x .
(5) Find the area bound by the graph of 2 x + y = 2 and the coordinate axes.

Calculus Review Worksheet
(6) Find '( x)
F if
F (x)
=
1
∫sec
( 2x)
t
2
dt
−1
(7) Find the total area bound by each of the following curves please.
(a)
2
y = x and y = x + 2
(b)
y
2
2 −
= 6x − x and y = x 2x
(c)
2
x = y and
x
=
3
−
2
2y
(d) y = sin(x) , and y = sin(2x) if
0
≤
x
≤
π
2
(e) y tan ( x)
= , y = 0 , and
x
=
π
4
(f)
y
3
2
= x + x − 2x , and y = − x + x + 6x
3
2
−x
(g) Calculator Problem y = 2 , and y = 3x 2 (Correct to 5 decimal places)
2 −

Calculus Review Worksheet
Answers
256
(1) (a) 15
(e) ln(2)
18
(b) 7
(f) 6
π
(c) 16
3
(g) 2
π
(d)
1− π
(h) π
4
(2) 9
56
(3) π
6
37
(4) 12
(5) 3
2

Calculus Review Worksheet
Answers
(6) '( x)
F = –2 csc(2x)
(7) (a)
9
2
(b)
64
3
(c) 4
(d) 2
5
(e)
1
−
π
4
(f) 16
(g) 4.28533