Questions from General Calculus

Q: Find the exact length of the curve. x = y3

Find the exact length of the curve. x = y3/2, 0 < y < 1

Q: Find the average value of the function on the given interval.

Find the average value of the function on the given interval.

Q: f (x) = 2x/ (1 + x2)

f (x) = 2x/ (1 + x2)2, [0, 2] (a). Find the average value of f on the given interval. (b). Find such that fave = f (c). (c). Sketch the graph of f and a rectangle whose area is the same as the area u...

Q: Use either a CAS or a table of integrals to find the

Use either a CAS or a table of integrals to find the exact length of the curve.

Q: A hawk flying at 15m/s at an altitude of 180

A hawk flying at 15m/s at an altitude of 180 m accidentally drops its prey. The parabolic trajectory of the falling prey is described by the equation y = 180 – x2/45 until it hits the ground, where is...

Q: The region bounded by the given curves is rotated about the specified

The region bounded by the given curves is rotated about the specified axis. Find the volume of the resulting solid by any method.

Q: Let I = f40 f(x) dx, where f

Let I = f40 f(x) dx, where f is the function whose graph is shown. (a). Use the graph to find L2, R2, and M2. (b). Are these underestimates or overestimates of I? (c). Use the graph to find T2. How...

Q: Find the interval [a, b] for which the value

Find the interval [a, b] for which the value of the integral fba (2 + x – x2) dx is a maximum.

Q: Find the average value of the function on the given interval.

Find the average value of the function on the given interval.

Q: Find the total length of the astroid x = a cos3θ,

Find the total length of the astroid x = a cos3θ, y = sin3θ, where a > 0.