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The Trapezoid Rule
Related Topics
Wize University Calculus 1 Textbook > Integration Techniques
The Trapezoid Rule
3 Activities
Which of the following is the integral approximation of
∫
1
3
cos
(
x
3
)
d
x
\int_1^3 \cos (x^3)dx
∫
1
3
cos
(
x
3
)
d
x
using the trapezoid rule with
n
=
3
n=3
n
=
3
?
2
3
[
cos
1
3
+
2
cos
(
5
/
3
)
3
+
2
cos
(
7
/
3
)
3
+
cos
(
9
/
3
)
3
]
\frac{2}{3}\left[\cos1^3+2\cos(5/3)^3+2\cos(7/3)^3+\cos(9/3)^3\right]
3
2
[
cos
1
3
+
2
cos
(
5/3
)
3
+
2
cos
(
7/3
)
3
+
cos
(
9/3
)
3
]
2
3
[
2
cos
1
3
+
2
cos
(
5
/
3
)
3
+
2
cos
(
7
/
3
)
3
+
2
cos
(
9
/
3
)
3
]
\frac{2}{3}\left[2\cos1^3+2\cos(5/3)^3+2\cos(7/3)^3+2\cos(9/3)^3\right]
3
2
[
2
cos
1
3
+
2
cos
(
5/3
)
3
+
2
cos
(
7/3
)
3
+
2
cos
(
9/3
)
3
]
1
3
[
2
cos
1
3
+
2
cos
(
5
/
3
)
3
+
2
cos
(
7
/
3
)
3
+
2
cos
(
9
/
3
)
3
]
\frac{1}{3}\left[2\cos1^3+2\cos(5/3)^3+2\cos(7/3)^3+2\cos(9/3)^3\right]
3
1
[
2
cos
1
3
+
2
cos
(
5/3
)
3
+
2
cos
(
7/3
)
3
+
2
cos
(
9/3
)
3
]
2
3
[
cos
1
3
+
cos
(
5
/
3
)
3
+
cos
(
7
/
3
)
3
+
cos
(
9
/
3
)
3
]
\frac{2}{3}\left[\cos1^3+\cos(5/3)^3+\cos(7/3)^3+\cos(9/3)^3\right]
3
2
[
cos
1
3
+
cos
(
5/3
)
3
+
cos
(
7/3
)
3
+
cos
(
9/3
)
3
]
1
3
[
cos
1
3
+
2
cos
(
5
/
3
)
3
+
2
cos
(
7
/
3
)
3
+
cos
(
9
/
3
)
3
]
\frac{1}{3}\left[\cos1^3+2\cos(5/3)^3+2\cos(7/3)^3+\cos(9/3)^3\right]
3
1
[
cos
1
3
+
2
cos
(
5/3
)
3
+
2
cos
(
7/3
)
3
+
cos
(
9/3
)
3
]
I don't know
Check Submission
More The Trapezoid Rule Questions:
Practice: Trapezoid Rule
Which of the following is the integral approximation of
∫
0
π
sin
(
x
)
d
x
\int_0^\pi \sin (x)dx
∫
0
π
sin
(
x
)
d
x
The Trapezoid Rule
Use The Trapezoid Rule to approximate
∫
2
5
1
x
−
1
d
x
\int_2^5\frac{1}{x-1}dx
∫
2
5
x
−
1
1
d
x
using 4 subintervals
The Trapezoid Rule
Approximate the following using a Trapezoid approximation with 6 subintervals.
∫
0
π
sin
x
d
x
\int_0^{\pi}\sin xdx
∫
0
π
sin
x
d
x
The Trapezoid Rule
Approximate
∫
1
5
1
+
x
2
d
x
\displaystyle\int\limits_{1}^{5}\sqrt{1+x^{2}}\,dx
1
∫
5
1
+
x
2
d
x
using the Trapezoidal Rule with
n
=
8
n=8
n
=
8
(answer correct to 2 decimal places).