Calculus Answers

Integrals Giving Inverse Trigonometric Functions

∫ dt/√(9t²-16)

Integrals Giving Inverse Trigonometric Functions

∫ dx/√(9-x²)

a solid of constant density is bounded below by the plane z = 0 , on the sides by the ellptical cylinder x^2 + 4y^2 = 4, and above by the plane z = 2 - x . calculate a) volume b) center of mass c) moment of inertial about x-axis , y-axis and z-axis

A solid of constant density is bounded below by the plane z = 0 , on the sides by the ellptical cylinder x^2 + 4y^2 = 4 , and above by the plane z = 2 - x .

Calculate

a) Volume

b) Center of mass

c) Moment of inertial about x-axis , y-axis and z-axis

A solid of constant density is bounded below by the plane z = 0 , on the sides by the ellptical cylinder x^2 + 4y^2 = 4, and above by the plane z = 2 - x .

Calculate

a) Volume

b) Center of mass

c) Moment of inertial about x-axis , y-axis and z-axis

With the help of triple integrals, find the volume of the sphere ρ = 2 in a) Rectangular coordianates b) Cylinderical coordiantes c) Spherical coordinates 

Find the center of mass of the region bounded by y=x^2 and y=6-x.

Find the center mass of the region bounded by y=e^2x and y=-cos(πx) between - 1/2 ≤x≤1/2.

Use the method cylinders to determine the volume of the solid obtained by rotating the region bounded by the given curves about the given axis of y=e^1/2 x/x+2, y=5 - 1/4 x, x=-1 abd x=6 about the line x=-2.

For the function below find the inverse.

a. 𝑓(𝑥) = (𝑥 − 2) 5 + 3

b. 𝑔(𝑥) = 4 𝑥+2

c. ℎ(𝑥) = 4 − √4𝑥 3 2

d. 𝑓(𝑥) = 4𝑥 3 + 2