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How do I find the area under a curve between two points?

Assuming you know the equation of the line, this could possibly be done in several ways. If you are able to integrate the equation of the line definitely using your current knowledge, then do this between th...
RR
Answered by Reece R. • Maths tutor
5351 Views

What is the point of differentiation?

Differentiation is a very useful concept; informally it tells us how 'fast' something is changing. A real-life example is given by the first and second derivatives of distance with respect to time: the first...
JH
Answered by Jake H. • Maths tutor
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A factory produces cartons each box has height h and base dimensions 2x, x and surface area A. Given that the capacity of a carton has to be 1030cm^3, (a) Using calculus find the value of x for which A is a minimum. (b) Calculate the minimum value of A.

To calculate the minimum value of A we first need to establish an equation for A. The surface area of a cuboid is relatively simple to figure out we simply work out the area of the faces and sum them togethe...
JC
Answered by Jacob C. • Maths tutor
5037 Views

Solve the simultaneous equations y + 4x + 1 = 0 and y^2 + 5x^2 + 2x = 0

y=-4x-1 (-4x-1)^2 +5x^2 +2x=0 16x^2 +8x +1 +5x^2 +2x=0 21x^2 +10x + 1 =0 (7x+1)(3x+1)=0 x=-1/7 or -1/3 y= -3/7 or 1/3
DJ
Answered by Dinesh J. • Maths tutor
15732 Views

The curve A (y = x3 – x2 + x -1) is perpendicular to the straight-line B at the point P (5, 2). If A and B intersect at P, what is the equation of B? Also, find any stationary points of the curve A.

Firstly find the gradient of A, through differentiation: dy/dy = 3x 2 – 2x + 1. To find the gradient at P, substitute the x value of the P coordinate into this equation: dy/dx = 3(2) 2 – 2(2) + 2 = 12 – 4 + ...
JS
Answered by James S. • Maths tutor
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