Curve Area Gold

\(\text{Find the area between the lines}\)

\(\text{Find the area between the lines:}\quad\phantom{\rule{0ex}{0ex}}y=-{x}^{3}+19{x}^{2}-114x+216\quad\phantom{\rule{0ex}{0ex}}y={x}^{2}-10x+24\quad\phantom{\rule{0ex}{0ex}}\text{intersecting at }\left(6,0\right)\text{, }\left(8,8\right)\text{ and }\left(4,0\right)\)

\(\text{Find the area between the lines:}\quad\phantom{\rule{0ex}{0ex}}y=-{x}^{3}-10{x}^{2}-33x-36\quad\phantom{\rule{0ex}{0ex}}y={x}^{2}+5x+4\quad\phantom{\rule{0ex}{0ex}}\text{intersecting at }\left(-2,-2\right)\text{, }\left(-4,0\right)\text{ and }\left(-5,4\right)\)

\(\text{Find the area between the lines:}\quad\phantom{\rule{0ex}{0ex}}y=-{x}^{3}-19{x}^{2}-114x-216\quad\phantom{\rule{0ex}{0ex}}y={x}^{2}+13x+36\quad\phantom{\rule{0ex}{0ex}}\text{intersecting at }\left(-4,0\right)\text{, }\left(-7,-6\right)\text{ and }\left(-9,0\right)\)

\(\text{Find the area between the lines:}\quad\phantom{\rule{0ex}{0ex}}y={x}^{3}+7{x}^{2}+7x-15\quad\phantom{\rule{0ex}{0ex}}y={x}^{2}+4x-5\quad\phantom{\rule{0ex}{0ex}}\text{intersecting at }\left(-2,-9\right)\text{, }\left(1,0\right)\text{ and }\left(-5,0\right)\)

\(\text{Find the area between the lines:}\quad\phantom{\rule{0ex}{0ex}}y=-{x}^{3}+4{x}^{2}-x-6\quad\phantom{\rule{0ex}{0ex}}y=2{x}^{2}-4x-6\quad\phantom{\rule{0ex}{0ex}}\text{intersecting at }\left(3,0\right)\text{, }\left(0,-6\right)\text{ and }\left(-1,0\right)\)

\(\text{Find the area between the lines:}\quad\phantom{\rule{0ex}{0ex}}y={x}^{3}-2{x}^{2}-5x+6\quad\phantom{\rule{0ex}{0ex}}y=2{x}^{2}-8x+6\quad\phantom{\rule{0ex}{0ex}}\text{intersecting at }\left(3,0\right)\text{, }\left(1,0\right)\text{ and }\left(0,6\right)\)

\(\text{Find the area between the lines:}\quad\phantom{\rule{0ex}{0ex}}y=-{x}^{3}+2{x}^{2}+5x-6\quad\phantom{\rule{0ex}{0ex}}y={x}^{2}-x-6\quad\phantom{\rule{0ex}{0ex}}\text{intersecting at }\left(3,0\right)\text{, }\left(0,-6\right)\text{ and }\left(-2,0\right)\)

\(\text{Find the area between the lines:}\quad\phantom{\rule{0ex}{0ex}}y=-{x}^{3}-{x}^{2}+9x+9\quad\phantom{\rule{0ex}{0ex}}y={x}^{2}-9\quad\phantom{\rule{0ex}{0ex}}\text{intersecting at }\left(3,0\right)\text{, }\left(-2,-5\right)\text{ and }\left(-3,0\right)\)

\(\text{Find the area between the lines:}\quad\phantom{\rule{0ex}{0ex}}y=-{x}^{3}+4{x}^{2}-x-6\quad\phantom{\rule{0ex}{0ex}}y=2{x}^{2}-4x-6\quad\phantom{\rule{0ex}{0ex}}\text{intersecting at }\left(3,0\right)\text{, }\left(0,-6\right)\text{ and }\left(-1,0\right)\)

\(\text{Find the area between the lines:}\quad\phantom{\rule{0ex}{0ex}}y=-{x}^{3}+15{x}^{2}-71x+105\quad\phantom{\rule{0ex}{0ex}}y={x}^{2}-10x+21\quad\phantom{\rule{0ex}{0ex}}\text{intersecting at }\left(7,0\right)\text{, }\left(4,-3\right)\text{ and }\left(3,0\right)\)

\(\text{Find the area between the lines:}\quad\phantom{\rule{0ex}{0ex}}y={x}^{3}+4{x}^{2}-x-4\quad\phantom{\rule{0ex}{0ex}}y={x}^{2}-1\quad\phantom{\rule{0ex}{0ex}}\text{intersecting at }\left(-1,0\right)\text{, }\left(1,0\right)\text{ and }\left(-3,8\right)\)

\(\text{Find the area between the lines:}\quad\phantom{\rule{0ex}{0ex}}y={x}^{3}+7{x}^{2}+7x-15\quad\phantom{\rule{0ex}{0ex}}y={x}^{2}+2x-3\quad\phantom{\rule{0ex}{0ex}}\text{intersecting at }\left(1,0\right)\text{, }\left(-3,0\right)\text{ and }\left(-4,5\right)\)

\(\text{Find the area between the lines:}\quad\phantom{\rule{0ex}{0ex}}y=-{x}^{3}-12{x}^{2}-39x-28\quad\phantom{\rule{0ex}{0ex}}y=2{x}^{2}+22x+56\quad\phantom{\rule{0ex}{0ex}}\text{intersecting at }\left(-3,8\right)\text{, }\left(-4,0\right)\text{ and }\left(-7,0\right)\)

\(\text{Find the area between the lines:}\quad\phantom{\rule{0ex}{0ex}}y=-{x}^{3}-6{x}^{2}-11x-6\quad\phantom{\rule{0ex}{0ex}}y={x}^{2}+x-6\quad\phantom{\rule{0ex}{0ex}}\text{intersecting at }\left(0,-6\right)\text{, }\left(-3,0\right)\text{ and }\left(-4,6\right)\)

\(\text{Find the area between the lines:}\quad\phantom{\rule{0ex}{0ex}}y=-{x}^{3}+7{x}^{2}-7x-15\quad\phantom{\rule{0ex}{0ex}}y={x}^{2}-2x-3\quad\phantom{\rule{0ex}{0ex}}\text{intersecting at }\left(4,5\right)\text{, }\left(3,0\right)\text{ and }\left(-1,0\right)\)

\(\text{Find the area between the lines:}\quad\phantom{\rule{0ex}{0ex}}y=-{x}^{3}-11{x}^{2}-31x-21\quad\phantom{\rule{0ex}{0ex}}y={x}^{2}+8x+7\quad\phantom{\rule{0ex}{0ex}}\text{intersecting at }\left(-4,-9\right)\text{, }\left(-1,0\right)\text{ and }\left(-7,0\right)\)

\(\text{Find the area between the lines:}\quad\phantom{\rule{0ex}{0ex}}y={x}^{3}+14{x}^{2}+64x+96\quad\phantom{\rule{0ex}{0ex}}y={x}^{2}+10x+24\quad\phantom{\rule{0ex}{0ex}}\text{intersecting at }\left(-3,3\right)\text{, }\left(-4,0\right)\text{ and }\left(-6,0\right)\)

\(\text{Find the area between the lines:}\quad\phantom{\rule{0ex}{0ex}}y=-{x}^{3}-13{x}^{2}-50x-56\quad\phantom{\rule{0ex}{0ex}}y={x}^{2}+11x+28\quad\phantom{\rule{0ex}{0ex}}\text{intersecting at }\left(-3,4\right)\text{, }\left(-4,0\right)\text{ and }\left(-7,0\right)\)

\(\text{Find the area between the lines:}\quad\phantom{\rule{0ex}{0ex}}y=-{x}^{3}-13{x}^{2}-56x-80\quad\phantom{\rule{0ex}{0ex}}y={x}^{2}+7x+10\quad\phantom{\rule{0ex}{0ex}}\text{intersecting at }\left(-3,-2\right)\text{, }\left(-5,0\right)\text{ and }\left(-6,4\right)\)

\(\text{Find the area between the lines:}\quad\phantom{\rule{0ex}{0ex}}y=-{x}^{3}-18{x}^{2}-107x-210\quad\phantom{\rule{0ex}{0ex}}y={x}^{2}+11x+30\quad\phantom{\rule{0ex}{0ex}}\text{intersecting at }\left(-5,0\right)\text{, }\left(-6,0\right)\text{ and }\left(-8,6\right)\)

\(\text{Find the area between the lines:}\quad\phantom{\rule{0ex}{0ex}}y={x}^{3}+{x}^{2}-9x-9\quad\phantom{\rule{0ex}{0ex}}y={x}^{2}-2x-3\quad\phantom{\rule{0ex}{0ex}}\text{intersecting at }\left(3,0\right)\text{, }\left(-1,0\right)\text{ and }\left(-2,5\right)\)

\(\text{Find the area between the lines:}\quad\phantom{\rule{0ex}{0ex}}y=-{x}^{3}-5{x}^{2}+x+5\quad\phantom{\rule{0ex}{0ex}}y={x}^{2}+4x-5\quad\phantom{\rule{0ex}{0ex}}\text{intersecting at }\left(-2,-9\right)\text{, }\left(1,0\right)\text{ and }\left(-5,0\right)\)

\(\text{Find the area between the lines:}\quad\phantom{\rule{0ex}{0ex}}y=-{x}^{3}+7{x}^{2}-14x+8\quad\phantom{\rule{0ex}{0ex}}y={x}^{2}-6x+8\quad\phantom{\rule{0ex}{0ex}}\text{intersecting at }\left(2,0\right)\text{, }\left(4,0\right)\text{ and }\left(0,8\right)\)

\(\text{Find the area between the lines:}\quad\phantom{\rule{0ex}{0ex}}y={x}^{3}+4{x}^{2}-4x-16\quad\phantom{\rule{0ex}{0ex}}y={x}^{2}+2x-8\quad\phantom{\rule{0ex}{0ex}}\text{intersecting at }\left(-1,-9\right)\text{, }\left(2,0\right)\text{ and }\left(-4,0\right)\)

\(\text{Find the area between the lines:}\quad\phantom{\rule{0ex}{0ex}}y=-{x}^{3}+17{x}^{2}-87x+135\quad\phantom{\rule{0ex}{0ex}}y={x}^{2}-12x+27\quad\phantom{\rule{0ex}{0ex}}\text{intersecting at }\left(9,0\right)\text{, }\left(4,-5\right)\text{ and }\left(3,0\right)\)