Use the fundamental theorem of calculus to find the area under the curve

Question

Use the Fundamental Theorem of Calculus to find the "area under curve" of  between  and .

Answer 1

The fundamental theorem of calculus says that where F'(x) = f(x) then:

_a∫^b f(x)dx = F(b) - F(a)

So find the antiderivative of 6x + 2. That would be the function, F(x), that when you take the derivative of it, that derivative is "6x + 2".

That would be 3x² + 2x so the area under the curve is 3x² + 2x evaluated between 3 and 5:

[3(5)² + 2(5)] - [3(3)² + 2(3)] = 85 - 33 = 52