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By expressing cos(2x) in terms of cos(x) find the exact value of the integral of cos(2x)/cos^2(x) between the bounds pi/4 and pi/3.

cos(2x)=cos 2 (x)-sin 2 (x)=2cos 2 (x)-1 Therefore:cos(2x)/cos 2 (x)=(2cos 2 (x)-1)/cos 2 (x)=2cos 2 (x)/cos 2 (x) - 1/cos 2 (x)=2 - 1/cos 2 (x)=2 - sec 2 (x) Integral of sec 2 (x) = tan(x) Integral of 2 = 2...
HF
Answered by Hugo F. • Maths tutor
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How do I differentiate an expression of the form y = (ax+b)^n?

In order to differentiate this we need to use the chain rule- first let u = ax + b. Then differentiating, du/dx = a. By substituting into the original expression, we can obtain y = u^n. Differentiating that ...
SC
Answered by Sam C. • Maths tutor
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Find dy/dx if y= sinx/2x+1

The quotient rule will need to be applied here.let u = sinx and let v = 2x+1du/dx = cosx and dv/dx =2thus using the quotient rule: (vdu/dx- udv/dx)/v^2(2xcosx +cosx - 2sinx)/ (2x+1)^2
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Answered by Sam T. • Maths tutor
5390 Views

Solve the inequality |4x-3|<|2x+1|.

There are two ways to solve this problem. The easiest way is graphically, but that requires little explanation and I am not sure how to show graphs on here so I will explain it algebraically.Because both sid...
NH
Answered by Nathanael H. • Maths tutor
9442 Views

Use the substitution u=2+ln(t) to find the exact value of the antiderivative of 1/(t(2+ln(t))^2)dt between e and 1.

The first step is to differentiate the substitution.Because u=2+ln(t) we can differentiate to get du=(1/t) dt which can be rearranged to dt=t du.Once we have this we can start on the actual expression. We st...
NH
Answered by Nathanael H. • Maths tutor
6640 Views