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A definite integral is actually a numerical value, which the represents the area under a graph between two points. For example, if you integrated f(x) between two values (lets call them a and b), the answ...

In this example, we want to find values for both x and y which are our unknowns. 

So we start by rearranging x to be on its own but still in terms of y. We then can plot it into the next ...

First combine the two functions so that we have an equation for a to solve:

G(h(a)) = (3^x)^3 + 1 = 3^(3x) + 1 = 244

which gives

3^(3x) = 243

Now...

Using the equation Area = 1/2 * base * height:

Area = 1/2 * 7 * 6

Area = 21 units.

First, we differentiate y = x^2 + 3x + 2 to find the slope of the curve at any given x point:

dy/dx = 2x + 3

So at x = 1, dy/dx = 2 + 3 = 5

We know that straig...