 Hello students, let's work out the following problem. It says find the area of the region bounded by y square is equal to 4x, x is equal to 1, x is equal to 4 and the x-axis is in the first quadrant. So let's now move on to the solution. Now we have to find the area bounded by the parabola y square is equal to 4x line, x is equal to 1, x is equal to 4 and the x-axis So this is the parabola y square is equal to 4x and this is the line x is equal to 1 and this is the line x is equal to 4 and we have to find area bounded by the parabola the line x is equal to 1, x is equal to 4 and the x-axis in the first quadrant. So we need to find area of this region right Now y square is equal to 4x so this implies y is equal to 2 root x Now the required area denoted by a is given by integral 1 to 4 because x is going from 1 to 4 y dx, now y is 2 root x dx, if taken just the positive square root it gives us the area in the first quadrant. Now we'll integrate this now the integral of x to the power 1 by 2 is x to the power 1 by 2 plus 1 that is 3 by 2 upon 3 by 2 where the lower limit of x is 1 and the upper limit is 4 Now this is equal to 4 by 3 Now we'll put x is equal to 4 per first So we have 4 to the power 3 by 2 minus now we'll put x is equal to 1 so we have 4 by 3 into now 2 can be written as 4 can be written as 2 square 1 to the power 3 by 2 is 1 itself this becomes 2 to the power 3 minus 1 4 by 3 into 2 to the power 3 is 8 minus 1 becomes 4 by 3 into 7 so the required area is 7 into 4 by 3 that is 28 by 3 Hence the required area is 28 by 3 square units. It's the version and the session by for now take care have a good day