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Intergrate ln(x) with resepct to x

To integrate this, we use the product rule. Think of it as intergrate [ 1 x ln (x)]. As by the product rule we chose one to intergrate and one to differentiate. We intergrate 1 to get x. We differentiate ln ...
LP
Answered by Leo P. • Maths tutor
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Find the roots of the equation y=x^2-8x+5 by completing the square.

Firstly, we need to look at completing the square. This is done by looking at the x^2-8x section of the equation. We need to find a way of converting it to the format of (x-a)^2. If you remember, when multip...
AG
Answered by Aaron G. • Maths tutor
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Solve the equation " 2sec^2(x) = 5tanx " for 0 < x < π

Firstly, we must recognise that the equation contains two different trigonometric functions (sec() and tan()) and therefore we must rewrite one of these functions in terms of the other. Therefore we will nee...
JB
Answered by Joel B. • Maths tutor
16010 Views

Solve for 0<=θ<π, the equation sin3θ-(sqrt3)cosθ=0 (C2)

Rearrange the equation to give sin3θ=(sqrt3)cos3θ, then divide through by cos3θ to give sin3θ/cos3θ=sqrt3. We know from our trig identities that sinx/cosx=tanx, so our equation now becomes tan3θ=sqrt3. Use y...
BH
Answered by Becky H. • Maths tutor
10059 Views

Express 2/P(P-2) in Partial Fractions (C4)

To start off with let 2/P(P-2)=A/P + B/(P-2) making the RHS of the equation one fraction gives : (A(P-2)+B(P))/P(P-2). So now we can compare the numerators (as the denominators are the same): A(P-2)+B(P)=2. ...
BH
Answered by Becky H. • Maths tutor
9999 Views