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Find ∫ ( 2x^4 - 4x^(-0.5) + 3 ) dx

When integrating, you need to add one to the power and divide the term by the power. We will consider each term individually, 2x⁴ will become (2x⁴⁺¹)/(4+1) = (2x⁵)/5, -4x<...

Answered by Rebecca M. • Maths tutor

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A curve has equation y = f(x) and passes through the point (4,22). Given that f'(x) = 3x^2 - 3x^(1/2) - 7 use intergration to find f(x).

As f '(x) is the differential of f(x) we have to first integrate f '(x). To do this we take each term individually and integrate it. So starting with 3x², to integrate a simple function of x li...

Answered by Jonathan O. • Maths tutor

6892 Views

how do you do binomial expansion when the power is a negative

There is a simple equation, similar to the normal binomial expansion, thats easy to remember once youve used it a few times.

(1+x)ⁿ=1+nx+{[n(n-1)]/2!}x²+{[n(n-1)(n-2)]/3!}x

Answered by Sarah M. • Maths tutor

7752 Views

Why does differentiation give us the results that it does?

A quick analysis here is based on the fact that y=(x²). A big change is worked out between two points. The gradient between x=1 and x=2 is equal to 3. BUT we know the gradient is constantly cha...

Answered by Alexander A. • Maths tutor

3281 Views

If I have a picture of a graph f(x), how can I draw what |f(x)| and 3f(x-2) look like?

This is about a topic called graph transformations. It can get quite complicated, but the lucky thing here is that each question can be broken down into steps.

So considering the first question wit...

Answered by Jamie H. • Maths tutor

6647 Views