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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 xx, we first let y = xx. (Note that xx is not in the form xc w...
The main piece of information this question gives us is that the two lines do not cross or touch. From this we can immediately see that we will need to use the discriminant of the quadratic formula b...
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