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Differentiate (x^0.5)ln(x) with respect to x.

First it's helpful to write f(x) = (x^0.5)ln(x)The product rule is useful here, this may be written in the form (u(x) v(x))' = u(x) v'(x) + u'(x) v(x).Here we will take u(x) = x^0.5 and v(x) = ln(x), meaning...
CC
Answered by Connor C. • Maths tutor
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Find the range of a degree-2 polynomial function such as 2x^2 +1, or x^2 + 2x - 3.

There are 3 methods for finding the range of a polynomial fucntion. This is good news because if you arrive at the same answer using these methods you wil be more confident that it is the correct answer.The ...
DH
Answered by Douglas H. • Maths tutor
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What is the double angle formula?

The double angle formula is how to combine/split trigonometric functions so that they can be integrated or simplified using identities. For example, cos (a+b)= cos(a)cos(b) - sin(a)sin(b) , which can be exte...
RW
Answered by Robert W. • Maths tutor
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The finite region S is bounded by the y-axis, the x-axis, the line with equation x = ln4 and the curve with equation y = ex + 2e–x , (x is greater than/equal to 0). The region S is rotated through 2pi radians about the x-axis. Use integration to find the

formula for volume of solid generated = 2pi x integral between limits of y 2 expand ( e x + 2e -x ) 2 = e 2x +4+4e -2x integrate e 2x +4+4e -2x with respect to x= 1/2(e 2x ) + 4x - 2e -2x (+C) however c won'...
KT
Answered by Kit T. • Maths tutor
7919 Views

Integrate the function xsin(4x^2) with respect to x, using the integration by substitution method.

Heres our integral: int(xsin(4x 2 )dx)The first decision to make is what to use as our substitution. We're going to go for the term tied up in the sine function: 4x 2 Set u = 4x 2 du/dx = 8x, therefore dx = ...
BC
Answered by Benjamin C. • Maths tutor
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