What is the area under the curve y = sin(x) from x = 0 to x = p?
0
1
p
2p
Correct Answer :
B. 1
Related Questions
What is the integral of vx with respect to x?
(2/3)x^(3/2) + C
(1/2)x^(3/2) + C
2vx + C
x^(3/2) + C
What are the parametric equations for a circle of radius r centered at the origin in polar coordinates?
x = rcos(?), y = rsin(?)
x = rcos(t), y = rsin(t)
x = r?, y = r?
x = cos(?), y = sin(?)
The solution to the logistic differential equation dy/dx = ky(1 - y) is often used to model population growth. What happens to the population when y = 1?
The population is increasing.
The population is decreasing.
The population is zero.
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What is the equation of a sphere with center (1, -2, 3) and radius 4?
(x - 1)^2 + (y + 2)^2 + (z - 3)^2 = 4
(x - 1)^2 + (y + 2)^2 + (z - 3)^2 = 16
(x + 1)^2 + (y - 2)^2 + (z + 3)^2 = 4
(x + 1)^2 + (y - 2)^2 + (z + 3)^2 = 16
What is the integral of 3x^2 with respect to x?
x^3 + C
x^2 + C
x^3/3 + C
3x + C
Which test can be used to determine the convergence of a series when its terms are all positive?
Alternating Series Test
Ratio Test
Integral Test
Comparison Test
What is the area under the curve y = sin(x) from x = 0 to x = p?
0
1
p
2p
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<1, 1>
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<4/5, -3/5>
<0, 0>
A ball is thrown into the air, and its height (in meters) above the ground at time t (in seconds) is given by h(t) = 4.9t^2 + 15t + 2. What is its initial velocity?
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15 m/s
2 m/s
0 m/s
If a plane is defined by the equation 2x - 3y + z = 7, what is the normal vector to the plane?
<2, -3, 1>
<3, 2, -1>
<1, 3, -2>
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If the rate of change of a quantity is given by f'(t) and ?(0 to 4) f'(t) dt = 10, what can you conclude about the quantity at t = 4?
The quantity is 10 at t = 4.
The quantity is 0 at t = 4.
The quantity is increasing at t = 4.
Nothing about the quantity at t = 4 can be determined.
The function P(t) represents the population of a city at time t. What does ?(a to b) P(t) dt represent?
The average population of the city on [a, b]
The change in population of the city from time a to time b
The rate of population growth at time a
The population of the city at time b
What is the antiderivative of e^(2x) with respect to x?
e^(2x) + C
(1/2)e^(2x) + C
(1/2)e^(2x^2) + C
(1/4)e^(2x) + C
If a car's speed is decreasing over time, what can you conclude about its acceleration?
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The acceleration is negative.
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Nothing about the acceleration can be determined.
If f(x) = x^3 + 2x^2 - 5x + 1, what is f''(x)?
3x^2 + 4x - 5
6x + 4
6x^2 + 4
3x^2 + 4
Which method is commonly used to solve separable differential equations?
Laplace transforms
Substitution
Separation of variables
Variation of parameters
What does the second derivative of a function represent?
The slope of the tangent line
The area under the curve
The concavity of the curve
The average rate of change
The definite integral ?(1 to 3) 2x dx is equal to:
4
8
6
10
Which type of differential equation is represented by the equation dy/dx = k*y, where k is a constant?
Separable
Linear
Exact
Homogeneous
What does the definite integral ?(a to b) f(x) dx represent geometrically?
The average value of f(x) on [a, b]
The area between the curve y = f(x) and the x-axis on [a, b]
The derivative of f(x) at x = a
The slope of the tangent line to the curve y = f(x) at x = b
What is the integral of 1/(x^2 + 1) with respect to x?
arctan(x) + C
ln(x^2 + 1) + C
2arctan(x) + C
(1/2)ln(x^2 + 1) + C
Which of the following functions is continuous at x = 2?
f(x) = 1/x
g(x) = x^2 + 3x + 2
h(x) = |x - 2|
None of the above
What is the particular solution to the initial value problem dy/dx = 2x, y(0) = 1?
y = x^2 + 1
y = x^2
y = 2x + 1
y = 2x
The cost C(x) of producing x units of a product is given by C(x) = 3x^2 + 2x + 7. What is the marginal cost when x = 5?
47
37
27
17
Which trigonometric substitution is commonly used to integrate rational functions involving v(a^2 - x^2)?
u = sin(x)
u = cos(x)
u = sec(x)
u = tan(x)
What is the volume of the region bounded by the surfaces z = x^2 + y^2 and z = 4 - x^2 - y^2?
4p
8p
16p
32p
What is the limit of (sin x) / x as x approaches 0?
1
0
-1
Undefined
What is a vector?
A point in space
A scalar quantity
A quantity with magnitude and direction
A constant value
What is the area of the region enclosed by the polar curve r = 2sin(?)?
p square units
4 square units
2 square units
0 square units
If the velocity of an object is given by v(t) = 3t^2, what does ?(1 to 2) v(t) dt represent?
The total distance traveled by the object from t = 1 to t = 2
The acceleration of the object at t = 1
The change in velocity of the object from t = 1 to t = 2
The displacement of the object at t = 2