The figure shows the curve x = y^{2}-9. Find the area of the region bounded by the curve, y-axis and the line y=4

# Category Archives: Integration and its applications

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 – x^{2} + 6 – 3x)

=6x – x^{3} – x^{2}

Differentiate y=5x(e^{3x}) with respect to x and hence find ∫x(e^{3x}) dx

Solution: 1/3(x)(e^{3x}) – 1/9(e^{3x}) + C

Y = 5x e^{3x}

dy/dx = 5x(e^{3x})(3) + 5 e^{3x}

dy/dx = 15x(e^{3x}) + 5(e^{3x})

∫15x(e^{3x}) + 5(e^{3x}) dx = 5x(e^{3x})

∫15x(e^{3x}) dx + (5(e^{3x}))/3 = 5x(e^{3x})

15∫x(e^{3x}) dx = 5x(e^{3x}) – 5/3(e^{3x})

∫x(e^{3x}) dx = 1/3(x)(e^{3x}) – 1/9(e^{3x}) + C