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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∫ y 2 dx (with upper and lower bounds of 3π/4 and π/4 respectively) to calculate the volume of th...
NC
Answered by Nicholas C. • Maths tutor
3851 Views

How can I find the equation of a line l which passes through the points (5,7) and (3, -1)

First thing first, we should always write down the equation of a straight line (which is y = mx + c ) as this will be important for this question.In order to find the equation of the straight line l we need ...
KC
Answered by Katie C. • Maths tutor
10281 Views

Differentiate xe^2

Use product rule. d(uv)/dx = u dv/dx +v du/dxu=x du/dx=1v=e^x dv/dx=e^x d(xe^x)/dx = xe^x + e^x.1 = e^x(x+1)
GB
Answered by George B. • Maths tutor
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A curve, C, has equation y =(2x-3)^5. A point, P, lies on C at (w,-32). Find the value of w and the equation of the tangent of C at point, P in the form y =mx+c.

To find the value of w, let x = w and y = -32. Substitute these values into the equation of the curve, C: y = (2x-3)^5 => -32 = (2(w) - 3 )^5. Note: the symbol, =>, means "implies that." Fift...
LM
Answered by Lewis M. • Maths tutor
4571 Views

A curve has equation y = f(x) and passes through the point (4, 22). Given that f ′(x) = 3x^2 – 3x^(1/2) – 7, use integration to find f(x), giving each term in its simplest form.

Firstly we can use the difference rule to split f'(x) into three components which we can consider separately. Then using the knowledge that the integral of x^n is 1/(n+1)*x^(n+1) we get the expression for f(...
AS
Answered by Abbey S. • Maths tutor
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