Curve Area Bronze

\(\text{Find the area between the lines:}\quad\phantom{\rule{0ex}{0ex}}y={x}^{2}-10x+21\quad\phantom{\rule{0ex}{0ex}}y=-x+7\quad\phantom{\rule{0ex}{0ex}}\text{intersecting at }\left(7,0\right)\text{ and }\left(2,5\right)\)

\(\text{Find the area between the lines:}\quad\phantom{\rule{0ex}{0ex}}y={x}^{2}+12x+32\quad\phantom{\rule{0ex}{0ex}}y=x+8\quad\phantom{\rule{0ex}{0ex}}\text{intersecting at }\left(-3,5\right)\text{ and }\left(-8,0\right)\)

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

\(\text{Find the area between the lines:}\quad\phantom{\rule{0ex}{0ex}}y={x}^{2}+12x+32\quad\phantom{\rule{0ex}{0ex}}y=-x-4\quad\phantom{\rule{0ex}{0ex}}\text{intersecting at }\left(-4,0\right)\text{ and }\left(-9,5\right)\)

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

\(\text{Find the area between the lines:}\quad\phantom{\rule{0ex}{0ex}}y=2{x}^{2}+17x+35\quad\phantom{\rule{0ex}{0ex}}y=-2x-4\quad\phantom{\rule{0ex}{0ex}}\text{intersecting at }\left(-3,2\right)\text{ and }\left(-6\frac{1}{2},9\right)\)

\(\text{Find the area between the lines:}\quad\phantom{\rule{0ex}{0ex}}y=\frac{1}{2}{x}^{2}+\frac{3}{2}x-5\quad\phantom{\rule{0ex}{0ex}}y=-x-7\quad\phantom{\rule{0ex}{0ex}}\text{intersecting at }\left(-1,-6\right)\text{ and }\left(-4,-3\right)\)

\(\text{Find the area between the lines:}\quad\phantom{\rule{0ex}{0ex}}y=2{x}^{2}-12x+16\quad\phantom{\rule{0ex}{0ex}}y=x-2\quad\phantom{\rule{0ex}{0ex}}\text{intersecting at }\left(4\frac{1}{2},2\frac{1}{2}\right)\text{ and }\left(2,0\right)\)

\(\text{Find the area between the lines:}\quad\phantom{\rule{0ex}{0ex}}y={x}^{2}-11x+24\quad\phantom{\rule{0ex}{0ex}}y=-x+3\quad\phantom{\rule{0ex}{0ex}}\text{intersecting at }\left(7,-4\right)\text{ and }\left(3,0\right)\)

\(\text{Find the area between the lines:}\quad\phantom{\rule{0ex}{0ex}}y={x}^{2}-9x+14\quad\phantom{\rule{0ex}{0ex}}y=-x-1\quad\phantom{\rule{0ex}{0ex}}\text{intersecting at }\left(5,-6\right)\text{ and }\left(3,-4\right)\)

\(\text{Find the area between the lines:}\quad\phantom{\rule{0ex}{0ex}}y=\frac{1}{4}{x}^{2}-\frac{7}{2}x+10\quad\phantom{\rule{0ex}{0ex}}y=-\frac{1}{2}x+5\quad\phantom{\rule{0ex}{0ex}}\text{intersecting at }\left(10,0\right)\text{ and }\left(2,4\right)\)

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

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

\(\text{Find the area between the lines:}\quad\phantom{\rule{0ex}{0ex}}y=\frac{1}{2}{x}^{2}-\frac{13}{2}x+15\quad\phantom{\rule{0ex}{0ex}}y=-\frac{1}{2}x+5\quad\phantom{\rule{0ex}{0ex}}\text{intersecting at }\left(10,0\right)\text{ and }\left(2,4\right)\)

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

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

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

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

\(\text{Find the area between the lines:}\quad\phantom{\rule{0ex}{0ex}}y={x}^{2}-13x+40\quad\phantom{\rule{0ex}{0ex}}y=\frac{1}{2}x+5\quad\phantom{\rule{0ex}{0ex}}\text{intersecting at }\left(10,10\right)\text{ and }\left(3\frac{1}{2},6\frac{3}{4}\right)\)

\(\text{Find the area between the lines:}\quad\phantom{\rule{0ex}{0ex}}y={x}^{2}-13x+40\quad\phantom{\rule{0ex}{0ex}}y=x-5\quad\phantom{\rule{0ex}{0ex}}\text{intersecting at }\left(9,4\right)\text{ and }\left(5,0\right)\)

\(\text{Find the area between the lines:}\quad\phantom{\rule{0ex}{0ex}}y=4{x}^{2}+14x+10\quad\phantom{\rule{0ex}{0ex}}y=x+7\quad\phantom{\rule{0ex}{0ex}}\text{intersecting at }\left(-\frac{1}{4},6\frac{3}{4}\right)\text{ and }\left(-3,4\right)\)

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

\(\text{Find the area between the lines:}\quad\phantom{\rule{0ex}{0ex}}y={x}^{2}-8x+7\quad\phantom{\rule{0ex}{0ex}}y=-2x-1\quad\phantom{\rule{0ex}{0ex}}\text{intersecting at }\left(4,-9\right)\text{ and }\left(2,-5\right)\)

\(\text{Find the area between the lines:}\quad\phantom{\rule{0ex}{0ex}}y=2{x}^{2}-9x+10\quad\phantom{\rule{0ex}{0ex}}y=2x-2\quad\phantom{\rule{0ex}{0ex}}\text{intersecting at }\left(4,6\right)\text{ and }\left(1\frac{1}{2},1\right)\)