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Integration by parts follows the general form: ∫u (dv/dx) = u.v - ∫v (du/dx)Let x = uLet sin 7x = (dv/dx)∫x.sin(7x) dx = x.(-1/7)cos(7x) - ∫(-1/7)cos(7x).1 dx = (-x/7)cos(7x) + (1/49)sin(7x) + c

First work out the area of the triangular face using the formula 1/2 A B sin c:1/2 x 1.4 x 1.4 sin(34) = 0.548m²
recall volume of a regular prism = area of face x length
hence V = 0.5...

a² + 2ab + b²

This question requires us to know how to multiply out the brackets and collect like terms together. It is worth 3 marks in total. First, we draw a smiley face on the brackets in the question: link the x a...

The substitution method means we have to rearrange the linear equation to find a variable, either x or y, then substitute it into the quadratic (and more difficult to solve) equation, as follows...x^2...