Sma 2277 calculus assignment - using integration determine

Question

CALCULUS ASSIGNMENT -

Q1. Find the total differential of w = x³yz + xy + z + 3 at (x, y, z) = (1, 2, 3).

Q2. Find the value of the double integral ∫∫_R(6x + 2y²)dA where R = {(x, y)| - 2 ≤ y ≤ 1, y² ≤ x ≤ 2 - y.

Q3. Find the reduction formula of I_n = ∫xⁿe^x dx hence evaluate I₄ = ₀∫¹x⁴e^xdx.

Q4. Using integration determine the position of the centroid of a plate whose shape is the region bounded by y = 2x², the -axis and the ordinates x = 0 and x = 3.

Q5. Find the volume of the solid bounded by the planes x = 0, y = 0, z = 0 and 2x + y + z = 4.