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How do you integrate (sinx)^3 dx?

Firstly, we must use the special property of trig functions which means that (sinx) n is the same as sin n x. Likewise, (cosx) n =cos n x, (tanx) n =tan n x and so on. In this case, we need to start by repla...
SS
Answered by Shanti S. • Maths tutor
8962 Views

Show that 2(1-cos(x)) = 3sin^2(x) can be written as 3cos^2(x)-2cos(x)-1=0.

Firstly let's expand out the staring equation getting rid of any brackets. This gives: 2-2cos(x)) = 3sin^2(x). Now we can spot that the sin^2(x) term is in the first equation but no the final one. So let's t...
RS
Answered by Rebekah S. • Maths tutor
4337 Views

Given two functions x = at^3 and y = 4a, find dy/dx

Solution: Parametric Differentiation with utilisation of Chain Rule. By the chain rule: dy/dx = dy/dt * dt/dx Note: dt/dx = 1 / (dx/dt) So dy/dt = 0, dx/dt = 3at^2 So dy/dx = 0 * 1/(3at^2) and hence dy/dx = 0.
MP
Answered by Michele P. • Maths tutor
3913 Views

How do I solve a cubic?

You can solve a cubic by applying factor theorem. This is where you plug different values for x into your cubic f(x) = ax^3 + bx^2 + cx + d such that x is a factor of d, until you find a value t for which f(...
HW
Answered by Harry W. • Maths tutor
3966 Views

Find the area under the curve of y=1/(3x-2)^0.5 between the limits x=1 and x=2 and the line y=0

This question requires integration since the area under the curve is equal to the integral between these bounds. Initially let u=3x-2 and differentiate with respect to x so then du/dx = 3. Rearrange to dx =d...
CT
Answered by Callum T. • Maths tutor
3707 Views