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Integrate (12x^5 - 8x^3 + 3)dx giving the terms of the answer in the simplest terms

Integration is essentially differentiation in reverse! So in the simpler cases instead of multiplying by the power of x and subtracting one from the power of x, you add one to the power of x and divide by...

Answered by Ellen S. • Maths tutor

6228 Views

(C3) Show that 4csc^2(x) - cot^2(x) = k can be expressed as sec^2(x) = (k-1)/(k-4) where k != 4

The student can answer this in several ways. One using the simple, known identities csc= 1/sin, cot=1/tan, sec=1/cos, tan=sin/cos, sin^2 + cos^2 = 1 and basic algebra is the following:
4csc^2 - cot^2...

Answered by Fearghus H. • Maths tutor

3499 Views

Find the binomial expansion of (-8+4x)^(2/3) up to and including the term in x^2.

The formula booklet is useful for this type of question, but only once we've rearranged the expression into the correct form. The formula booklet expression is: (1 + z)^n = 1 + nz + 0.5n*(n-1)

Answered by David M. • Maths tutor

4005 Views

y = 2x^3 + 15x^2 + 24x + 10 Find the stationary points on this curve and determine their nature

First differentiate the function to obtain
dy/dx = 6x^2 + 30x + 24
Then set this equal to 0 and solve to find the x values of the stationary points
6x^2 + 30x + 24 = 0
6(x^2 + 5x + 4) ...

Answered by Kate W. • Maths tutor

9855 Views

Show that (1 - cos(2x)) / (1 + cos(2x)) = sec^2(x) - 1

First, take the side of the equation that looks most complicated because it often needs simplifying. This is the LHS in this case. The LHS has cos(2x) twice - therefore the double angle formula probably a...

Answered by Louis G. • Maths tutor

6392 Views