Questions from General Calculus

Q: Use Simpson’s Rule with n = 10 to estimate the volume obtained

Use Simpson’s Rule with n = 10 to estimate the volume obtained by rotating about the y-axis the region under the curve y = √1 + x3, 0 < x < 1.

Q: If the region shown in the figure is rotated about the y

If the region shown in the figure is rotated about the y-axis to form a solid, use Simpson’s Rule with n = 10 to estimate the volume of the solid.

Q: Set up an integral that represents the length of the curve.

Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places.

Q: Set up an integral that represents the length of the curve.

Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places.

Q: Let f (x) = 0 if is any rational number

Let f (x) = 0 if is any rational number and f (x) = 1 if is any irrational number. Show that f is not integrable on [0, 1].

Q: Set up an integral that represents the length of the curve.

Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places.

Q: The figure shows a region consisting of all points inside a square

The figure shows a region consisting of all points inside a square that are closer to the center than to the sides of the square. Find the area of the region.

Q: Set up an integral that represents the length of the curve.

Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places.

Q: Find the exact length of the curve. x = 1

Find the exact length of the curve. x = 1 + 3t2, y = 4 + 2t3, 0 < t < 1

Q: Find the exact length of the curve. y2 = 4

Find the exact length of the curve. y2 = 4 (x + 4)3, 0 < x < 2, y > 0