The figure shows the curve x = y2-9. Find the area of the region bounded by the curve, y-axis and the line y=4

Find the total area enclosed by the curve y = x(x+3)(2-x), the x-axis and the line x=4 solution: 21(1/12) units x(2x – x2 + 6 – 3x) =6x – x3 – x2

Differentiate y=5x(e3x) with respect to x and hence find ∫x(e3x) dx Solution: 1/3(x)(e3x) – 1/9(e3x) + C Y = 5x e3x dy/dx = 5x(e3x)(3) + 5 e3x dy/dx = 15x(e3x) + 5(e3x) ∫15x(e3x) + 5(e3x) dx = 5x(e3x) ∫15x(e3x) dx + (5(e3x))/3 = 5x(e3x) 15∫x(e3x) dx = 5x(e3x) – 5/3(e3x) ∫x(e3x) dx = 1/3(x)(e3x) – 1/9(e3x) + […]