603 Answered Questions for the topic AP Calculus

#### Find the area of the region bounded by the graphs of y = -x^2 + 2x + 3 and y = 3.

Question options:
1)
1.333
2)
4.500
3)
7.333
4)
-4.333

#### Help with curves please!

Find the number b such that the line y = b divides the region bounded by the curves y = x2 and y = 4 into two regions with equal area. Give your answer correct to 3 decimal places.

#### Help with curves please!

Find the area of the region bounded by the graphs of y = x, y = -x + 4, and y = 0.Options:
1)
1
2)
2
3)
4
4)
None of these

#### Help with curves please!

Find the area of the region bounded by the graphs of y = x2 - 4x and y = x - 4. Options:
1)
-4.500
2)
4.500
3)
2.333
4)
None of these

#### Help with curves please!

Which integral gives the area of the region in the first quadrant bounded by the x-axis, y = x2, and x + y = 2?Options:
1}
2)
3)
4)

#### Help with curves please!

Which of the following integrals represents the area of the region bounded in the first quadrant by x = and the functions f(x) = sec2(x) and g(x) = sin(x)?Options:
1)
2)
3)
4)

#### Does Mean Value Theorem apply to the functions

Determine if the Mean Value Theorem for Integrals applies to the function f(x) = 5 - x2 on the interval . If so, find the x-coordinates of the point(s) guaranteed by the theorem.Question...
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#### Find the Average Value

Find the average value of over the interval [1, 3].Question options:
1)
1.10
2)
2.20
3)
0.55
4)
0.33

02/24/20

#### Help with Definite Integral

Write the Riemann sum to find the area under the graph of the function f(x) = x3 from x = 2 to x = 5.options:
1.
2)
3)
4)

#### The base of a solid in the xy-plane is the circle x^2 + y^2 = 16. Cross sections of the solid perpendicular to the y-axis are equilateral triangles. What is the volume, in cubic units, of the solid?

Question options:
1)
2)
3)
4)

02/24/20

#### Please help with Definite Integrals

The Riemann sum, , is equivalent to with .Write the integral that produces the same value as . options:
1)
2)
3)
4)

#### Which of the following integrals will find the volume of the solid that is formed when the region bounded by the graphs of y = e^x, x = 1, and y = 1 is revolved around the line y = -2.

Which of the following integrals will find the volume of the solid that is formed when the region bounded by the graphs of y = ex, x = 1, and y = 1 is revolved around the line y = -2.Question...
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#### The region in the first quadrant bounded by the x-axis, the line x = π, and the curve y = sin(sin(x)) is rotated about the x-axis. What is the volume of the generated solid?

Question options:
1)
1.219
2)
3.830
3)
1.786
4)
5.612

#### Find the area or the region bounded by the curves y = x^3 and y = 9x.

Question options:
1)
0
2)
10.13
3)
40.50
4)
20.25

Ap Calculus Calculus

02/22/20

#### for what value of x is the line tangent to y=x^2 parallel to the line tangent to y= √ x

#### How long till the ball reaches its highest point

An elementary student kicks a ball straight into the air with a velocity of 16 feet/sec. If acceleration due to gravity is -32 ft/sec2, how many seconds after it leaves his foot will it take the...
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#### Find the displacement

For an object whose velocity in ft/sec is given by v(t) = -t2 + 4, what is its displacement, in feet, on the interval t = 0 to t = 3 secs?Question...
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#### Find the distance

Find the distance, in feet, a particle travels in its first 4 seconds of travel, if it moves according to the velocity equation v(t)= -t2 + 4 (in feet/sec). Question...
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#### Find the velocity

Find the velocity, v(t), for an object moving along the x-axis if the acceleration, a(t), is a(t) = 3t2 + cos(t) and v(0) = 2. Question options:
1)
v(t) = t3 + sin(t) + 2
2)
v(t) = t3 -...
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#### Find the average value

Find the average value of f(x) = sin(x) over the interval [0, π].Question options:
1)
2
2)
2π
3)
4)
0

#### Find The Volume

The base of a solid in the region bounded by the two parabolas y2 = 8x and x2 = 8y. Cross sections of the solid perpendicular to the x-axis are semicircles. What is the volume, in cubic units, of...
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#### Find the volume of the solid formed by revolving the region bounded by the graphs of y = x^2, x = 3, and y = 4 about the y-axis.

Question options:
1)
2)
3)
4)
None of these

#### Find the Volume

Use your calculator to find the approximate volume in cubic units of the solid created when the region under the curve y = sec(x) on the interval [0,] is rotated around the x-axis.Question...
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