Search over 10,000 free study notes

The definite integral gives the value of the area bounded between the curve at the given limits, and the x-axis (if we are integrating with respect to x!) If this value is negative, it means that the area...

using the product rule

product rule is dy/dx=v.du/dx+u.dv/dx

let u = x^2 and v = cos(x)

du/dx=2x

dv/dx = -sin(x)

so dy/dx=2xcos(x)-x^2sin(x)

My exact explanation would depend on the students level of understanding. The following answer assumes a basic understanding of differentiation and equations of lines; a) Gradient of tangent is equal to g...

To differentiate x^x, we first let y = x^x. (Note that x^x is not in the form x^c w...