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Integrate 4x^3 - 3x + 6

When integrating an equation we can treat each variable individually. Lets start with 4x^3, when integrating, we raise the power (in this case 3) by +1 and divide the multiple (in this case 4) by the new rai...
BP
Answered by Bradley P. • Maths tutor
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Integrate the following expression with respect to x, (2+4x^3)/x^2

First we should simplify the expression to be able to integrate it. We should separate the expression to 2 parts. Now we have the following: 2/x^2 + 4xWe can bring the x^2 to the top,now we have the followin...
MP
Answered by Maria P. • Maths tutor
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Find the equation of the tangent to the curve y = x^2-2x-3 at x=-1

First we find the gradient by differentiation. Differentiating the expression for the curve gives dy/dx=2x-2. Subbing in x=-1 gives dy/dx=-4 so the gradient of the line is -4. To find the y intercept, we use...
CR
Answered by Caleb R. • Maths tutor
6367 Views

evaluate the integral 2x/((9+x^2)^1/2) between -2 and 0

One approach would be to use integration by parts, as we have two functions of x within the integral. This approach would get you to the answer but would be more difficult and convoluted than necessary. One ...
AF
Answered by Aiden F. • Maths tutor
4441 Views

The height x metres, of a column of water in a fountain display satisfies the differential equation dx/dt = 8sin(2t)/(3sqrt(x)), where t is the time in seconds after the display begins. (a) Solve the differential equation, given that x(0)=0

Our DE (Differential Equation) dx/dt = 8sin(2t)/(3sqrt(x)) is separable because dx/dt can be expressed as a product of two functions of the form dx/dt = f(t)g(x) = (8sin(2t)) * (1/(3sqrt(x))).To solve the DE...
JM
Answered by James M. • Maths tutor
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