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Integrate ln(x)

Our A-level knowledge does not give us any identities to be able to integrate this from memory. But what we do have from memory is that the derivative of ln(x) is 1/x. Why would this help us? Let's take a...

Answered by James E. • Maths tutor

2976 Views

Solve the following simultaneous equations: 6j+4k=40; 7j-3k=-7

j = 2, k = 7

Answered by Catherine E. • Maths tutor

2985 Views

Consider the unit hyperbola, whose equation is given by x^2 - y^2 = 1. We denote the origin, (0, 0) by O. Choose any point P on the curve, and label its reflection in the x axis P'. Show that the line OP and the tangent line to P' meet at a right angle.

We differentiate our equation with respect to x to find that 2x - 2y(dy/dx) = 0, and rearrange to find that dy/dx = x/y. We set P = (x, y). The slope of OP is given by y/x, and the slope of the tangent at...

Answered by Dylan C. • Maths tutor

3086 Views

Show that the volume of the solid formed by the curve y=cos(x/2), as it is rotated 360° around the x-axis between x= π/4 and x=3π/4, is of the form π^2/a. Find the constant a.

After sketching a diagram of the curve and the solid for clarity, we see that we need to use the formula V = π∫ y² dx (with upper and lower bounds of 3π/4 and π/4 respectively) to calculate the...

Answered by Nicholas C. • Maths tutor

3154 Views