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How do I tackle fractional powers?

The main thing to know when answering these sorts of questions is that the denominator of the fraction is the root you take of the given number. For example, 16^1/2 is the same as the sqaure roo...

Answered by Cameron S. • Maths tutor

2974 Views

Integrate sin(x)cos(x)^2 from 0 to π/2

Use substitution u=cos(x) resulting in du=-sin(x)dx: ∫₀^π/2sin(x)cos(x)^2dx = ∫₀^π/2-u^2du = [-1/3 u^3]_x=0^x=π/2 = [-1/3 cos(x)^3]₀

Answered by Benedek S. • Maths tutor

8186 Views

Solve the two equations: Equation 1: 2a - 5b = 11 Equation 2: 3a + 2b = 7

Firstly, you should aim to eliminate one of the unknown values. As b is positive and negative in each equation, this would be a good value to eliminate. Both equations would have to be multiplied to cance...

Answered by Ikraan H. • Maths tutor

6123 Views

How can I sketch a graph?

There are a number of steps before sketching a graph. We will look over bits of theory and then do some examples (I'll show the examples in the online lesson space) First we have to find the x-intercept a...

Answered by Razvan T. • Maths tutor

3108 Views

If y = exp(x^2), find dy/dx

Recall that the derivative of exp(x) is exp(x), but notice this question is slightly more complex due to the x^2 term. This is example of differentiationg composite functions, and so the chain rule is req...

Answered by Stuart B. • Maths tutor

7733 Views