Find the area of the region between the x-axis and \(y = (x - 1)^2\) from x = 0 to x = 2.
A1/3
B2/3
C1/2
D1/4
Mathematics · Question Bank
Integral Calculus
67 questions · page 4 of 4. Answer in your head first, then check the solution.
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
Find the volume (in cubic units) generated by rotating the circle \(x^2 + y^2 + 6x + 4y + 12 = 0\) about the y-axis.
A39.48
B59.22
C118.44
D29.61
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
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?
A186
B179
C181
D184