Find the area (in sq. units) bounded by the parabolas \(x^2-2y=0\) and \(x^2+2y-8=0\).
A11.7
B4.7
C9.7
D10.7
Mathematics · Question Bank
Integral Calculus
42 of 67 questions match · page 2 of 3. Answer in your head first, then check the solution.
Find the area of the curve \(r^2=a^2 \cos 2\theta\).
Aa
B2a
C\(a^2\)
D\(a^3\)
Locate the centroid of the plane area bounded by \(y=x^2\) and \(y=x\).
A0.4 from the x-axis and 0.5 from the y-axis
B0.5 from the x-axis and 0.4 from the y-axis
C0.5 from the x-axis and 0.5 from the y-axis
D0.4 from the x-axis and 0.4 from the y-axis
Find the coordinates of the centroid of the plane area bounded by the parabola \(y=4-x^2\) and the x-axis.
A(0,1)
B(0,1.6)
C(0,2)
D(1,0)
Locate the centroid of the plane area bounded by the equation \(y^2=4x\), \(x=1\) and the x-axis on the first quadrant.
A(3/4, 3/5)
B(3/5, 3/4)
C(3/5, 3/5)
D(3/5, 2/3)
The area enclosed by the ellipse \(\frac{x^2}{9}+\frac{y^2}{4}=1\) is revolved about the line \(x=3\). What is the volume generated?
A355.3
B360.1
C370.3
D365.1
The area bounded by the curve \(y^2=12x\) and the line \(x=3\) is revolved about the line \(x=3\). What is the volume generated?
A179
B181
C183
D185
Given the area in the first quadrant bounded by \(x^2=8y\), the line \(y-2=0\) and the y-axis. What is the volume generated when the area is revolved about the line \(y-2=0\)?
A28.41
B27.32
C25.83
D26.81
Find the volume (in cubic units) generated by rotating a circle \(x^2+y^2+6x+4y+12=0\) about the y-axis.
A39.48
B47.23
C59.22
D62.11
Given the area in the first quadrant by \(x^2=8y\), the line \(x=4\) and the x-axis. What is the volume generated by revolving this area about the y-axis.
A53.26
B52.26
C51.26
D50.26
Find the moment of inertia, with respect to x-axis of the area bounded by the parabola \(y^2=4x\) and the line \(x=1\).
A2.03
B2.13
C2.33
D2.53
Find the volume of the solid formed by revolving the area bounded by the curve \(y^2 = x^3(1 - x)\) in the first quadrant about the x-axis.
A0.137
B0.147
C0.157
D0.167
A particle moves on a straight line with a velocity \(v = (4 - 2t)^3\) at time t. Find the distance traveled from t = 0 to t = 3.
A32
B36
C34
D30
The area enclosed by the ellipse \(4x^2 + 9y^2 = 36\) is revolved about the line x = 3. What is the volume generated?
A370.3
B360.1
C355.3
D365.1
Find the area of one loop of \(r^2 = 16\sin 2\theta\).
A16
B8
C4
D6
Find the area bounded by \(y = 6x - x^2\) and \(y = x^2 - 4x\).
A125/3
B125/2
C100/3
D100/9
The vertical end of a water trough is an isosceles triangle with a width of 6 feet and a depth of 3 feet. Find the force on one end when the trough is filled with water.
A638 lbs
B683 lbs
C562 lbs
D526 lbs
The area enclosed by the ellipse \(4x^2 + 9y^2 = 36\) is revolved about the line x = 3. What is the volume generated?
A370.3
B360.1
C355.3
D365.1
Evaluate \(\displaystyle\int x\sin x\cos x\,dx\).
A\(-\tfrac{1}{4}x\cos 2x + C\)
B\(\tfrac{1}{8}x\sin 2x + C\)
C\(-\tfrac{1}{4}x\sin 2x + \tfrac{1}{8}x\cos 2x + C\)
D\(-\tfrac{1}{4}x\cos 2x + \tfrac{1}{8}\sin 2x + C\)
At t = 0, a particle starts at rest and moves along a line in such a way that at time t its acceleration is \(24t^2\) feet per second per second. Through how many feet does the particle move during the first 2 seconds?
A32
B48
C64
D96