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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
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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
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Distinguish, using examples, between economic regionalism and political regionalism?

Despite economics and politics often complimenting one another, when one refers to economic and political regionalism one must appreciate that these are two contrasting concepts. Economic regionalism is esse...
AW
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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
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How should I structure my A-level History essay?

The most important thing is to form a plan and know what your thoughts are on the question before you start writing. This will help you avoid going off on tangents in the main body of the essay. It is also i...
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Answered by Kate M. • History tutor
3008 Views