# Math Help - Calculate the area

1. ## Calculate the area

Calculate the area of the region limited by curves:

1) $y=x^3$ and $y=x^2+2x$

answer: $\frac{37}{12}$

2) $y=x^3-2x^2-5x+6$, the axis-x, $x=-1$ and $x=2$

answer: $\frac{157}{12}$

2. 1) Check where the two curves meet:

$x^3 = x^2 + 2x$ which gives three points: $x=-1, x=0, x=2$

So you need to split the integration area up into two parts:

$\int_{-1}^0 (x^3 - (x^2 + 2x))dx + \int_0^2 (x^2 + 2x - x^3) dx$

2) Check where the curve meets the x-axis:

$x^3 - 2x^2 -5x +6 = 0$

Same procedure as in (1).