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)
Area of required region = 2 (Area in the first quadrant)
Hence, This is the required Area of given equation.
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
The equation of AC is
4y - 4 = 3x - 12
Area of ∆ABC = Area under AB + Area under BC – Area under AC
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