Questions from General Calculus

Q: Calculate the double integral. ∬R tanθ/√(1-

Calculate the double integral. ∬R tanθ/√(1-t^2 ) dA, R = { (θ, t) | 0 < θ < π/3, 0 < t < 1/2}

Q: Calculate the double integral. ∬R x sin (x

Calculate the double integral. ∬R x sin (x + y) dA, R = [0, π/6] × [0, ×/3]

Q: Calculate the double integral. ∬R x/(1+

Calculate the double integral. ∬R x/(1+xy) dA, R = [0, 1] × [0, 1]

Q: Show that the maximum value of the function is a2 + b2

Show that the maximum value of the function is a2 + b2 + c2. Hint: One method for attacking this problem is to use the Cauchy-Schwarz Inequality: |a ∙ b |

Q: Calculate the double integral. ∬R ye-xy dA

Calculate the double integral. ∬R ye-xy dA, R = [0, 2] × [0, 3]

Q: Find the volume of the solid that lies under the plane 4x

Find the volume of the solid that lies under the plane 4x + 6y - 2z + 15 = 0 and above the rectangle R = {(x, y) | -1 < x < 2, -1 < y < 1j.

Q: Find the volume of the solid that lies under the hyperbolic paraboloid

Find the volume of the solid that lies under the hyperbolic paraboloid z = 3y2 - x2 + 2 and above the rectangle R = [-1, 1] × [1, 2].

Q: (a). Estimate the volume of the solid that lies below

(a). Estimate the volume of the solid that lies below the surface z = 1 + x2 + 3y and above the rectangle R = [1, 2] × [0, 3]. Use a Riemann sum with m = n = 2 and choose the sample points to be lower...

Q: Find the volume of the solid enclosed by the surface z =

Find the volume of the solid enclosed by the surface z = x2 + xy2 and the planes z = 0, x = 0, x = 5, and y = ±2.

Q: Find the volume of the solid enclosed by the surface z =

Find the volume of the solid enclosed by the surface z = 1 + x2yey and the planes z = 0, x = 61, y = 0, and y = 1.