Calculus Answers

The region in the first quadrant which is bounded by the curve y² =

4x, and the lines x = 4 and y = 0, is revolved about the x-axis.

Locate the centroid of the resulting solid of revolution.

Given the area in the first quadrant bounded by y^2 = x, the line x =

4 and the x-axis. What is the volume generated when this area is

revolved about the y-axis?

The loop of the curve has an equation of y² = x (1 - x)^2. Find the

area enclosed by the loop of the curve.

The curve has an equation y = e^x. Compute the area bounded by the

curve from x = 0 to x = 1.

The curve has an equation y = e*. Compute the area bounded by the

curve from x = 0 to x = 1.

A curve has an equation of y=sin x. If the area of the curve

y=sin x from x=0 to X=pi is revolved about the y-axis, what is the

volume generated?

Two curves having an equation of x=2√y and y=2√x intersect each

other. Compute the area between the two curves.

Find an equation of the line through the point (3, 5) that cuts off the least area from the first quadrant?

a) A plant grows 1.6 cm in the first week. Each week it grows by 5% more than it did the week before. Using geometric sequence find, how much it grows in the 6^th week.

b) In the year 2000 a shop sold 150 computers. Each year the shop sold 10 more computers than the year before. Show that the shop sold 220 computers in 2007.

c) How many students must be in a class to guarantee that at least two students receive the same score on the final exam if the exam is graded on a scale from 0 to 100 points?

Identify the surfaces of the following equations by converting them into equations in the Cartesian form.

ρ = sin ϕ sin θ