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How do you know when to integrate by parts?

This is usually a good idea if you have an integral with two functions multiplied together when one of the functions differentiates to a constant (could take more than one differentiation).For example to ...

Answered by Dominic H. • Maths tutor

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Where does the circle (x-6)^2+(y-7)^2=4 intersect with y=x+3

Where does the circle (x-6)²+(y-7)²=4 intersect with y=x+3We need to sub y=x+3 into the circle equation giving us an equation in just x:(x-6)²+(x-4)²=4Next we e...

Answered by Nicola L. • Maths tutor

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dh/dt = (6-h)/20. When t=0, h=1. Show that t=20ln(5/(6-h))

Part 1: This question requires us to first do some rearranging. The right hand side of the equation is in terms of h, and we are looking to find t in terms of h, so it won't be appropriate to simply integ...

Answered by Linetta A. • Maths tutor

3766 Views

How do you integrate (sinx)^3 dx?

Firstly, we must use the special property of trig functions which means that (sinx)ⁿis the same as sinⁿx. Likewise, (cosx)ⁿ=cosⁿx, (tanx)ⁿ=tan^n...

Answered by Shanti S. • Maths tutor

6635 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'...

Answered by Rebekah S. • Maths tutor

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