Calculus Answers

Evaluate the following integral.

∫(1 to 4)∫(0 to 4) (6x−3y)dxdy=

Calculate the double integral ∫∫R(8x+6y+48)dA where R is the region: 0≤x≤3,0≤y≤4.

Evaluate the following integral after converting to polar coordinates: (0 to 1) ∫ (y to sqrt(2-y^2)) ∫ (x+y) dx dy

Sketch the region of integration, carefully with appropriate labels, and then perform the following integral: (0 to pi/4) ∫ (4secƟ to 0) ∫ r dr dƟ

Evaluate ∫∫R cos(x^2+y^2)dA, where R is the region above the x-axis within the circle x^2+y^2= 25.

What is the volume of the region under the surface z=xy that lies over the triangle with vertices at the origin, (3, 0), and (0, 6)?

Evaluate ∫ ∫D (y/(x5+1)) dA on the region D defined by 0≤x≤1; 0≤y≤x2.

State true or false the function f defined by f (x)=| x − 2| is differentiable in [0 ,1 ].