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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

7733 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

5916 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

2928 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

7544 Views

What is the perimeter and area of a rectangle with a length of 8cm and width of 3cm?

The perimeter is the distance around the rectangle. A rectangle has 4 sides: 2 of them will be the length (8cm) and 2 of them the width (3cm). To get the perimeter, you add up 2 of the length and 2 of the...

Answered by Emma L. • Maths tutor

24824 Views