Find the area under the curve y=xexp(-x)
first recognise ‘area under’ = integrationfunction is a product so by partsset x=u; exp(-x)=dv/dx integral(udv/dx)=uv-integral(vdu/dx)
du/dx =1; v=-exp(-x)ans=(x.-exp(-x))-integral(1.exp(-x)dx)ans=-xexp(-x)+exp(-x)+C
Related Maths A Level answers
All answers ▸Use Implicit Differentiation to find dy/dx of the following equation: 3(x)^2 + 8xy + 5(y)^2 = 4
A sweet is modelled as a sphere of radius 10mm and is sucked. After five minutes, the radius has decreased to 7mm. The rate of decrease of the radius is inversely proportional to the square of the radius. How long does it take for the sweet to dissolve?
How do I integrate tan^2 x?
Find the gradient of a straight line with the points P(5,3) and Q(8,12)