The area bounded between the parabola y²=4 x and the line y =2 x -4 is equal to

Step-by-step solution

The point of intersection of y ²=4 x and y=2 x-4 is array cc & (2 x-4)²=4 x & x²-5 x+4=0 & (x-1)(x-4)=0 & x=1,4 & y=-2,4 Required area & = & _ -2 ⁴ ( y +4 2 ) dy - _ -2 ⁴ y ² 4 dy = & 1 2 [ y ² 2 +4 y ]_ -2 ⁴- 1 4 [ y ³ 3 ]_ -2 ⁴ = & 1 2 [8+16-(2-8)]- 1 12 [64+8] = & 1 2 [30]- 1 12 (72) = & 15-6=9 sq unit array