Find the area under the curve y = (4x^3) + (9x^2) - 2x + 7 between x=0 and x=2

To be able to solve this, the equation needs to be integrated. To do this, increase the power by 1 and divide by the new power.

The equation below is equal to that given in the question

y = 4(x^3) + 9(x^2) - 2(x^1) + 7(x^0).

This makes it more clear how the integration is carried out to give

x^4 + 3(x^3) - x^2 + 7x.

To find the area, the new equation needs to be solved by substituting in x=2 and x=0.

For x=2,

((2)^4) + 3((2)^3) - (2)^2 + 7(2) = 16 + 24 - 4 + 14 = 50

For x=0,

((0)^4) + 3((0)^3) - (0)^2 + 7(0) = 0.

To find the area, value for the equation with the lower value of x needs to be taken from the one with the higher. Therefore the area is given by:

area = 50 - 0 = 50