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Solve the following equations. Leave answers in simplest terms a)e^(3x-9)=8. b) ln(2y+5)=2+ln(4-y)

a) Using log rules, a^x=b becomes log(a)b=x. If we take ln of both sides, we get ln(e^(3x-9))=ln8. ln(e) =1, so we just get 3x-9=ln8. Now we can simply manipulate this to get x=(9+ln8)/3=3+(1/3)ln8. Another ...
BW
Answered by Ben W. • Maths tutor
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a) show that (cosx)^2=8(sinx)^2-6sinx can be written as (3sinx-1)^2=2 b)Solve (cosx)^2=8(sinx)^2-6sinx

Start with a). Looking at this equation, the trig identity screaming out is cosx^2+sinx^2=1--> cosx^2=1-sinx^2. Substituting this into the LHS of the equation, and with a bit of algebraic rearrangement, w...
BW
Answered by Ben W. • Maths tutor
25101 Views

Integrate xsin(2x) by dx between the limits 0 and pi/2.

First it is important to identify that this is an integration by parts question as it can't be solved by substitution. Let I = integral for ease of notation.Write out integration by parts formula I(u)dv= uv ...
BA
Answered by Benedict A. • Maths tutor
8666 Views

Integrate 3t^2 + 7t with respect to t, between 1 and three.

To integrate you add one to the power and divide by the new power, so this becomes:3t 3 /3 + 7t 2 /2 simplifying to t 3 + 7/2 t 2 If we were just performing indefinite integration you would need to remember ...
JM
Answered by Josh M. • Maths tutor
4072 Views

Integrate (lnx)/x^2 dx between limits 1 and 5

Let I = integral[(lnx)/x^2 dx] for simplicity.Firstly, we realise we must use integration by parts. This is:Integral [u(x)v'(x) dx] = u(x)v(x) - Integral[u'(x)v(x) dx]So we can see that, by letting u(x)=lnx ...
JL
Answered by Jimmy L. • Maths tutor
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