(x)
C)x sin (x)
)2x
D)1 + x2
D)x sin (x2 )
Quiz 24
cos (4xZ2 ) x C)8x3 cos (4x2 )
F (x)Example
=
11:+ t2 dt
Z 2 0
5x 3 dx
Math 1431
LAB session 15
D)32x3 cos (4x2 )
0
ZZ 40
p
p
3
dx2t dt
(x) =
tx2 +
Z
1x
5
3
+ 5x dx
x2
1
Z 1 Z 4x2
p
(x) = 4x3/2 +
t cos
dt
5 (t)
x dx
0
0
Z
3
6x(3 + 2x2 ) dx
) 1 C)x sin (x) D)x sin (x2 )
Z ⇡
2
sinx(x)
dx
x D)13 +
0
os (4x2 ) 16
C)8x3 cos (4x2 )
Z
2
5x
3 dx
0
Example
2:
Z
Z
Z
4
1
5
1
1
p
3 x dx
3
+ 5x dx
x2
p
3
4x /2 + 5 x dx
0
Z
3
6x(3 + 2x2 ) dx
1
Z
⇡
3 sin (x) dx
0
16
D)32x3 cos (4x2 )
5x x 3 dx
0
Z
4
p
3 x dx
1
Z 4x2
Z 5
F (x) =3 + 5xtdx
cos (t) dt
2 0
1 x
Z 1
p
3/2
4x + 5 x dx
n (x)0 C)x sin (x) D)x sin (x2 )
Z 3
++
2xx2 )2 dx
C)2x 6x(3
D)1
Example 3:
1
Z ⇡
2
3
2
x cos (4x
)
C)8x
cos
(4x
)
3 sin (x) dx
2
0
Z
Z
2
16
5x
3 dx
0
Z
4
p
3 x dx
1
5
3
+ 5x dx
2
x
1
Example
4:
Z 1
p
3/2
4x + 5 x dx
0
Z
3
6x(3 + 2x2 ) dx
1
Z
⇡
3 sin (x) dx
0
16
D)32x3 cos (4x2 )
x2 cos (4xZ2 )4x2 C)8x3 cos (4x2 )
Z x
F (x) =Question
t# cos (t)
dt
2
F (x)
1 + t dt
Z =0
5
3x
0
D)32x3 cos (4x2 )
4 dx
1
Z
16 p
C)x
sin (x)
(x)
D)x sin (x2 )
Z 50 px dx
1
2
F
(x)
=
t
2 + 2t dt
)2x ZD)1
6 x+ x
2
4x dx
x
12
cos (4x
) C)8x3 cos (4x2 )
Z 1
p
3/2
4xZ 4x
+2 5 x dx
0Z
5
F (x)
t cos (t) dt
Z =
3
(x)
4 dx
2
6x(3
+
2x
1
Question
# ) dx
1
Z
0
3x
Z
16
3⇡/2
p
dxdx D)x sin (x2 )
C)x
sinx(x)
(x)
55cos
⇡/21
2
C)2x Z 6D)1
2 16+ x
4x dx
x
1 2
x2 cos (4x
)
Z
C)8x3 cos (4x2 )
1
4x
0
Z
3
Z
3/2
p
+ 5 x dx
5
3x
4 dx
1
2
6x(3
+
2x
) dx
Z
16
1
p
5 x dx
Z
3⇡
Question
/2
1
#
Z 6 5 cos (x) dx
2
⇡/2
4x dx
x
1
16
Z 1
p
3/2
4x + 5 x dx
0
Z
3
6x(3 + 2x2 ) dx
1
Z
D)32x3 cos (4x2 )
3⇡/2
5 cos (x) dx
⇡/2
16
D)32x3 cos (4x2 )
Z
1 0
4x
3/2
p
+ 5 x dx
Example
5:
0
Z
x)
3
C)x
sin (x) 2 D)x sin (x2 )
6x(3 + 2x ) dx
1
2
+
x
ZD)1
⇡
3 sin (x) dx
2
cos (4x0 ) C)8x3 cos (4x2 )
)2x
Z
Z
Z
16
2
5x
3 dx
0
Z
4
p
3 x dx
1
5
1
3
+ 5x dx
x2
1
4x
3/2
p
+ 5 x dx
0
Z
3
1
6x(3 +6:2x
Example
Z
2
) dx
⇡
3 sin (x) dx
0
16
D)32x3 cos (4x2 )
x) =
Example 7:
Z
4
|x
1
3| dx
Z
4
Example 8: |x
Z
4
(
1
(
2x
3| dx1 if 0  x  2
9 3x if 2 < x < 3.
Z
1 if 30  x  2
f (x) dx
f (x)|x
=
1
3| dx
2x
9Find3x if0 2 < x < 3.
Z 3
f (x) dx
0
17
2x 1 if 0  x  2
9 3x if 2 < x < 3.
Z 3 9:
n (x)Example
C)x sin (x) D)x sin (x2 )
f (x) dx
(x) =
0
The graph
of function f(x) is given on the right.
Z x 2
C)2x
D)1 + x
F (x) =
2
f (t) dt
4
2
x cos (4x )
=
Z
Z
C)8x3 cos (4x2 )
5
3x
4 dx
1
Z
Z
Find F(3)
16
p
5 x dx
1
6
1
2
x
4x dx
3/2
p
1
4x
+ 5 x dx
0
Z
3
6x(3 + 2x2 ) dx
1
Question
#
Z
3⇡/2
5 cos (x) dx
⇡/2
16
17
Question #
Z
(
6
3
|x
5| dx
2x 1 if 0  x  2
9 3x if 2 < x < 3.
Z 3
f (x) dx
D)32x3 cos (4x2 )