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Complete the indefinite integral : ∫x lnx dx

Use the formula: ∫uv' dx = uv - ∫u'v dx (use I = the integral we're looking for)Note we cant integrate ln x easily but we can differentiate into 1/x so we use:u = ln x and v' = x we have u' = 1/x and v = x 2...
KD
Answered by Katy D. • Maths tutor
6667 Views

Solve the simultaneous equations: y - 3x + 2 = 0 y^2 - x - 6x^2 = 0

y = 3x -2(3x-2) 2 - x - 6x 2 = 0 9x 2 - 12x + 4 - x - 6x 2 = 03x 2 - 13x + 4 = 0(3x - 1)(x-4) = 0 x = 1/3 or x = 4then y = -1 when x = 1/3 and y = 10 for x = 4
KD
Answered by Katy D. • Maths tutor
10414 Views

Given y =( 2x+1 )^0.5 and limits x = 0 , x = 1.5 , find the exact volume of the solid generated when a full rotation about the x-axis .

Using V = pi* integral of y 2 between b and a with respect to x , where V is the volume of generated solid.y 2 = 2x + 1 Integrating between given limits yields a result of 3.75Multiplying through by pi leave...
DS
Answered by Dominik S. • Maths tutor
3466 Views

Differentiate y = 2xln(x)

This is an example of a question where you would use the product rule, where if y = uv then dy/dx = u dv/dx + v du/dx. In this case u = 2x and v = ln(x). So first of all we will differentiate 2x which is fai...
TW
Answered by Toby W. • Maths tutor
8590 Views

Factorise x^2+5X+6

(x+3)(x+2)To check this, use the 'FOIL' (first, outside, inside, last) method to ensure the answer is correct.x^2+2x+3x+6x^2+5x+6
DB
Answered by Darius B. • Maths tutor
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