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To do this, first draw a sketch of both graphs to see roughly what kind of result we should expect to get. We know that at the intersection points, the values of x and y for both graphs must be equal. so ...

Here we will use integration by parts because we have the product of two terms, x and 2^x. Using the integration by parts formula, we have to differentiate one of these terms and integrate the other. We c...

For this question, we have to integrate x² multiplied by sin(x). For integrating a product, you must use a method called integration by parts. Without bogging ourselv...

First we will rewrite y so it is written with a power: y=1/x²-2x-1=(x²-2x-1)^-1 Now let u=x²-2x-1 => du/dx = 2x -2 Writing y in terms of u: y=u^-1 =...

A 15% increase means that the £80,000 represents 115% of the original value.

Therefore what we do is:

£80,000=£125% divided by 125 

...