MATH 2414 Final Exam V2 Questions and 100% Correct Answers 2026/27 Update –
University of Houston.
Question number 1.
Your answer was B. Correct.
Set up the integral needed to find the area of the region bounded bewteen the graph of
f(x) = x2 + 3 x and g(x) = 10.
5
A ∫ (10 − 3 x − x2) dx
−2
2
B ∫ (10 − 3 x − x2) dx
−5
2
C ∫ (x2 + 3 x − 10) dx
−5
5
D ∫ (x2 + 3 x + 10) dx
0
5
E ∫ (x2 + 3 x + 10) dx
−2
Question number 2.
Your answer was A. Wrong.
MATH 2414 Final Exam
, Suppose that f(x) is continuous on [−2, 6] and f(x) < 0 on [−2, 6]. If the area between f(x)
and the x-axis on [−2, 6] is 10, then find the average value of f on this interval.
5
A
4
B 0
5
C —
2
5
D
2
5
E —
4
F −10
G None of the above.
Question number 3.
MATH 2414 Final Exam
, Your answer was A. Correct.
1
Find the area bounded by the curves y = 3 √x + 8 and y = x2 + 8 .
9
A 27
27
B
2
C −27
27
D —
2
E 54
Question number 4.
Your answer was B. Correct.
Sketch the region bounded by the curves x = y 3 , x = 1, and y = 0 then find the volume of the
solid generated by revolving this region about the y-axis.
34π
A
7
MATH 2414 Final Exam
, 6π
B
7
13π
C
7
20π
D
7
27π
E
7
Question number 5.
Your answer was D. Correct.
The base of a solid is the circle x2 + y 2 = 16. Find the volume of the solid given that the cross
sections perpendicular to the x-axis are isoceles right triangles with leg on the xy-plane.
518
A
3
524
B
3
515
C
3
MATH 2414 Final Exam
University of Houston.
Question number 1.
Your answer was B. Correct.
Set up the integral needed to find the area of the region bounded bewteen the graph of
f(x) = x2 + 3 x and g(x) = 10.
5
A ∫ (10 − 3 x − x2) dx
−2
2
B ∫ (10 − 3 x − x2) dx
−5
2
C ∫ (x2 + 3 x − 10) dx
−5
5
D ∫ (x2 + 3 x + 10) dx
0
5
E ∫ (x2 + 3 x + 10) dx
−2
Question number 2.
Your answer was A. Wrong.
MATH 2414 Final Exam
, Suppose that f(x) is continuous on [−2, 6] and f(x) < 0 on [−2, 6]. If the area between f(x)
and the x-axis on [−2, 6] is 10, then find the average value of f on this interval.
5
A
4
B 0
5
C —
2
5
D
2
5
E —
4
F −10
G None of the above.
Question number 3.
MATH 2414 Final Exam
, Your answer was A. Correct.
1
Find the area bounded by the curves y = 3 √x + 8 and y = x2 + 8 .
9
A 27
27
B
2
C −27
27
D —
2
E 54
Question number 4.
Your answer was B. Correct.
Sketch the region bounded by the curves x = y 3 , x = 1, and y = 0 then find the volume of the
solid generated by revolving this region about the y-axis.
34π
A
7
MATH 2414 Final Exam
, 6π
B
7
13π
C
7
20π
D
7
27π
E
7
Question number 5.
Your answer was D. Correct.
The base of a solid is the circle x2 + y 2 = 16. Find the volume of the solid given that the cross
sections perpendicular to the x-axis are isoceles right triangles with leg on the xy-plane.
518
A
3
524
B
3
515
C
3
MATH 2414 Final Exam
