AP Calculus AB Problems with Solutions (Part - 22)

Problem 1 :

The region enclosed by the graph of y = sin x and the lines y = 1/2, x = π/6 and x = 5π/6 is rotated about the x-axis. What is the volume of the solid generated?

Solution :

Problem 2 :

A)  ln 6

B)  ln √3

C)  1

D)  ln √3 - 1

Solution :

Problem 3 :

If f(x) = ³√(x² + 7) ⋅ e^x, then what is the value of f'(1)?

A)  3e/4

B)  7e/6

C)  3e/2

D)  13e/6

Solution :

Problem 4 :

At a musical concert the audience stands inside a semicircular area of radius 50 yards. The stage is also a semicircular shape of radius 10 yards. if the denisty of the audience at r yards from the center of the stage is given by f(r) people per square yard, which of the following expressions gives the number of people at the concert?

Solution :

Problem 5 :

If four subdivisions of [1, 3] are used, what is the trapezoidal approximation of the following definite integral?

A)  ½(cos 1 + √1.5 cos 1.5 + √2 cos 2 + √2.5 cos 2.5 + √3 cos 3)

B)  ½(cos 1 + 2√1.5 cos 1.5 + 2√2 cos 2 + 2√2.5 cos 2.5 + √3 cos 3)

C)  ¼(cos 1 + √1.5 cos 1.5 + √2 cos 2 + √2.5 cos 2.5 + √3 cos 3)

D)  ¼(cos 1 + 2√1.5 cos 1.5 + 2√2 cos 2 + 2√2.5 cos 2.5 + √3 cos 3)

Solution :

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