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  • Please help! The area in the first quadrant bounded by y = 4x2, x = 0 y = 1, and y = 4 is

The area in the first quadrant bounded by y = 4x2, x = 0 y = 1, and y = 4 is

  • Option 1)

    2 sq. units

  • Option 2)

    2\frac{1}{2}  sq. units

  • Option 3)

    2\frac{1}{3}\: \:  sq. units

  • Option 4)

    3 sq. units

 

Answers (1)

best_answer

As we learnt

Area along y axis -

Let y_{1}= f_{1}(x)\, and \, y_{2}= f_{2}(x) be two curve, then area bounded by the curves and the lines

y = a and y = b is

A=\int_{a}^{b}\left ( x_{2}-x_{1} \right )dy

- wherein

 

 Required \: area = \int_{1}^{4}xdy

=\int_{1}^{4}\frac{\sqrt{y}}{2}dy= \frac{1}{2}\left [ \frac{2}{3}y^{3/2} \right ]_{1}^{4}

=\frac{1}{3}\left [ 4^{3/2}-1 \right ]=2\frac{1}{3}sq.units

 


Option 1)

2 sq. units

Option 2)

2\frac{1}{2}  sq. units

Option 3)

2\frac{1}{3}\: \:  sq. units

Option 4)

3 sq. units

Posted by

gaurav

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