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Use the substitution u=1+e^x to find the Integral of e^(3x) / (1 + e^x)

e^x=u-1 so e^3x=(u-1)³ and du/dx = e^x so rearranging gives dx=e^-x du Substituting all that information in the integral we get Integral ( (u-1)^...

Answered by Ismet P. • Maths tutor

11455 Views

The gradient of the curve at point (x,y) is given by dy/dx = [7 sqrt(x^5)] -4. where x>0. Find the equation of the curve given that the curve passes through the point 1,3.

I like this question because it can be broken down into parts, each which contain an important reminder/lesson for an A level/GCE maths student. I would start the lesson by running through the rules of in...

Answered by Michael S. • Maths tutor

4540 Views

Find the turning points of the curve (x^3)/3 + x^2 -8x + 5

Step one, we need to assess what the question is asking us to do, in this case, find the turning points.The turning points on the graph are where the gradient is equal to zero, so in order to find the tur...

Answered by Ellie M. • Maths tutor

3389 Views

How would I go about finding the coordinates minimum point on the curve eg y = e^(x) - 9x -5?

In order to find the coordinates of the minimum point of any curve y = f(x), you must differentiate the equation of the curve with respect to x and then equate it to zero.In this case, the differential of...

Answered by Theo R. • Maths tutor

3681 Views

Identify two errors made by a student asked to evaluate the following integral (Will upload question to less space)

Error 1: expressed 3/x^(1/2) incorrectly. Should be 3x^-(1/2), not 3x^(1/2).Error 2: subtracted the larger area from the smaller area after substituting the unknowns with the given limits value.

Answered by Seun L. • Maths tutor

5238 Views