Q. 95.0( 1 Vote )

# Calculate the area under the curve included between the lines x = 0 and x = 1.

Answer :

y = 2√x

squaring both sides we get

⇒ y^{2} = 4x

y^{2} = 4x is a equation of parabola

In y^{2} = 4x parabola it is not defined for negative values of x hence the parabola will be to the right of Y-axis passing through (0, 0)

Now for y = 2√x x and y both has to be greater than 0 that is both positive hence both lie in 1^{st} quadrant

Hence y = 2√x will be parabolic curve of y^{2} = 4x only in 1^{st} quadrant

x = 0 is equation of Y-axis and x = 1 is a line parallel to Y-axis passing through (1, 0)

Plot equations y = 2√x and x = 1

So we have to integrate y = 2√x from 0 to 1

let us find area under parabola

⇒ y = 2√x

Integrate from 0 to 1

Hence area bounded = unit^{2}

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