# Area between 3 curves

I need to calculate an area between those 3 curves.

I have no idea what area should I calculate (because of y=-x-1)

Regards.

• What does the problem, itself, say? There may be other clues to tell you of which of the two regions you must calculate the area. – Cameron Buie Mar 16 '13 at 9:42

Simply compute $\int_a^0 [(x-1)^3 - 3\cdot x - 5] {d}x$ where a is intesect of $(x-1)^3$ with $3\cdot x - 5$(if in Wolfram|Alpha enter "$[solve (x-1)^3 = 3\cdot x - 5][1]$" you get $x = -1$ and $x = 2$, so $a = -1$): $\int_{-1}^0 [(x-1)^3 - 3\cdot x + 5] {d}x = \left.{{x}\over{4}}\cdot [(x - 4)\cdot x^2 + 16]\right|_{-1}^0 = {{11}\over{4}}$. If now in Wolfram|Alpha enter "solve 3\cdot x-5 = -x - 1" you get $x = 1$, so second part is ${4}\cdot \int_{0}^1 [- x + 1] {d}x = \left.-{2\cdot x}\cdot (x - 2)\right|_0^1 = 2$. Total is ${{11}\over{4}} + 2 = {{15}\over{4}}$