Pocketbook of Useful Formulæ and Memoranda
for Civil and Mechanical Engineers

630 moleswobth’s pocket-book Differential and Integbal Calculus—continued. dxn — nxn~1 dx-, nxl Simple Example of the Integra- tion between Fixed Limits. Let x and y be any co-ordinates. b and a = the greatest and least values of x. j'b y dx = the area of the figure cdef. . Application of the Calculus to Areas and Centres of Gravity. z — Area of one of the layers parallel to plane AB. x — Distance of centre of layer from the plane A B. dx = Thickness of one layer. V = Volume of the whole body == sum oi volumes of the layers ~fzdx. Distance of centre of gravity from fx zdx plane A B = —y— • Application of Calculus to Curves. Let AB, Ac, be the axes of the co-ordinates of the curve, a and y the co-ordinates. <p (x y)= 0 = the equation of the curve. Ian. o = -— dx