A-level questions

Integration: Find the following. The first is done for you.

 

 

 

 

 

 

 

 

 

Follow the following steps to perform a numerical integration. Copy and complete

 

 

 

Integrate and place in square brackets

 

Substitute in  and

 

 

 

 

Find the answer

 

Using the same layout and notation, find the following two definite integrals:

 

 

 

 

 

 

Integrating to solve differential equations

To solve

 

You are told that when ,

Integrate to find y

 

Substitute in  and

 

Use this to find c

Now, re-write equation for y with c inside

Use the same technique to solve the following differential equations

 

 

  

 

 

 

Trigonometry

Use the cosine rule to find the missing side

Find x

 

 

 

Find the area of the triangle