# How to solve this problem step by step with application of integration?

##### 3 Answers

#### Explanation:

First, let's find the

For

For

In order to calculate the requested area, our definite integral must then be evaluated in the interval

We can do this by halving the interval; by adding the area under

First, let's evaluate the indefinite integrals for each line:

and

Then, let's evaluate these integrals at the bounds mentioned earlier:

and

Finally, the area is the sum of these two values:

The answer is

#### Explanation:

So I'm gonna assume you don't know anything about integration.

The region is bounded by

First you need to find where the two lines cut the X-axis, you do that by replacing the

I really do hope i don't have to go any further then this, but if necessary i will help, I'm just having a bit of trouble with writing out the formulas.

#### Explanation:

We can calculate the given area by finding Area **A** and area **B** and adding these to find total area.

To find area **A** we need the upper and lower bounds. We can see where these are from the graph, but it is always best to find them algebraically, graphs are not normally accurate enough.

These can be found by solving:

Our upper bound is at the y axis,

So we need the integral:

Area

Plugging in upper and lower bounds:

Area

Area

For area **B**

The upper bound is:

So we need integral:

Area

Plugging in upper and lower bounds:

Area

Area

Total area: