Q. 275.0( 1 Vote )

# Find the area of

Given, A circle has equation 4x2 + 4y2 = 9 and a parabola x2 = 4y.

To Find: Find the area of a circle.

Explanation: We have a circle equation 4x2 + 4y2 = 9 and parabola x2 = 4y We can write the given equation as  - - - - (i)

And, x2 = 4y - - - - (ii)

Now, Put the value of x2 in equation (i)   2y(2y + 9) - 1(2y + 9) = 0

(2y + 9)(2y - 1) = 0 Here, We neglect the negative value Substitute the value of y in equation (ii)   Since,

Area of required region = 2 (Area in the first quadrant)      Hence, This is the required Area of given equation.

OR

Given, A triangle ABC , whose vertices are A(4, 1) , B(6, 6) and C(8, 4)

To Find: Find the area of triangle ABC using integration.

Explanation: We have three vertices of triangle A(4, 1) , B(6, 6) and C(8, 4). Now, The equation of line AB is,    2y - 2 = 5x - 20

2y = 5x - 18 Now, The equation of BC is  y - 6 = - 1(x - 6)

BC = y = 12 - x

Similarly,

The equation of AC is   4y - 4 = 3x - 12 Area of ∆ABC = Area under AB + Area under BC – Area under AC      square units

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