# Area bounded by the curves $4y = |{x^2} - 4|$ and $y + |x|\, = 7,$ is equal to Option 1) 8 sq. units Option 2) 16 sq. units Option 3) 4 sq. units Option 4) 32 sq. units

G gaurav

As we learnt

Area between two curves -

If we have two functions intersection each other.First find the point of intersection.  Then integrate to find area

$\int_{o}^{a}\left [ f\left ( x \right )-9\left ( x \right ) \right ]dx$

- wherein

Required area = $2\left( {\int\limits_0^2 {\left( {7 - x - \left( {\frac{{4 - {x^2}}}{4}} \right)} \right)\,dx + \int\limits_2^4 {\left( {7 - x - \left( {\frac{{{x^2} - 4}}{4}} \right)} \right)\,dx} } } \right)$

$=2\left( {\int\limits_0^2 {\left( {6 - x - \frac{{{x^2}}}{4}} \right)\,dx + \int\limits_2^4 {\left( {8 - x - \frac{{{x^2}}}{4}} \right)\,dx} } } \right)$
$=2\left( {6x - \frac{{{x^2}}}{2} + \frac{{{x^3}}}{{12}}} \right)_0^2 + 2\left( {8x - \frac{{{x^2}}}{2} - \frac{{{x^3}}}{{12}}} \right)_2^4 = 32\: sq. units$

Option 1)

8 sq. units

Option 2)

16 sq. units

Option 3)

4 sq. units

Option 4)

32 sq. units

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