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How do you integrate ln(x)?

I would use the whiteboard and write down y=lnx, and also the integration by parts formula below it. I would then explain how to treat ln(x) as the "u" and "1" as dv/dx; including why thi...
JZ
Answered by Jamie Z. • Maths tutor
4033 Views

How do you integrate xln(x) between the limits of 0 and 2?

In order to answer this question you need to use integration by parts.Using the standard integration by parts formula: ∫u dv/dx dx = uv-∫v du/dx dx.Let:u=ln(x) v=(1/2)x 2 du/dx=1/x dv/dx=xTherefore we get:I=...
LK
Answered by Lena K. • Maths tutor
2016 Views

If a rectangle has sides (x+3) and (2x-1) and an area of 15, find x and the length of each side.

To find x, we need to create an expression from the information given. We know the area is 15 and that the area is equal to the length multiplied by the width. This gives us:(x+3)(2x-1) = 15Then we can expan...
JL
Answered by Jasmin L. • Maths tutor
5369 Views

Enzymes are proteins. Antarctic fish may have different structure of enzymes to non-antarctic fish. Explain how their enzyme structure may be different.

Enzymes would have different sequence of amino acids and therefore different primary structure. This would result in different shape of a protein ie their tertiary or, if present, quaternary structure.
DR
Answered by Daria R. • Biology tutor
6461 Views

Work out: 3 ½ – 2 ⅓ Give your answer as a improper fraction

3 ½ = 7/22 ⅓ = 7/3To add or subtract 2 fractions, the denominator (bottom number) must be the same. To create a common denominator we can multiply the first fraction by 3 and the second by 2.This gives us 7/...
MS
Answered by Mai S. • Maths tutor
8712 Views