Top answers

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
1905 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
5222 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
8583 Views

Solve 5x^2 = 10x + 4 , to 2 decimal places.

First rearrange to get 5x 2 - 10x - 4 = 0 , by subtracting 10x and 4 from both sides of the equation. Here, we can use the quadratic formula which is x = -b+- sqrt(b 2 -4ac) / 2a. In our question a=5 , b=-10...
AP
Answered by Alexander P. • Maths tutor
15576 Views

find the gradient of the tangent to the curve y=x^2 at the point (4,16)

First of all you must differentiate this function, as this will give you the gradient function necessary to find the gradient at the point (4,16). To differentiate it you use the formula dy/dx= a n x (n-1) ,...
JM
Answered by Jessica M. • Maths tutor
8704 Views