The area bounded by the curve ay = x² and the lines y = a and y = 4a is [tex]\mathbf{ \dfrac{14a^2}{3} }[/tex]
The area bounded by the curve can be determined by taking the integral of the curve such that: [tex]\mathbf{\int^{2a}_{a} x dy}[/tex]
From the given information:
[tex]\mathbf{\implies \int^{4a}_{a} (ay)^{1/2} \ dy}[/tex]
[tex]\implies \mathbf{ a^{1/2} \int^{4a}_{a} y^{1/2} \ dy}[/tex]
Applying power rule
[tex]\implies \mathbf{ a^{1/2} \Big[\dfrac{2}{3}y^{3/2}\Big] ^{4a}_0 }[/tex]
Taking the boundaries, we have:
[tex]\implies \mathbf{ a^{1/2}\dfrac{14}{3}a^{5/2} }[/tex]
[tex]\implies \mathbf{ \dfrac{14a^2}{3} }[/tex]
Learn more about the area bounded by the curve here:
https://brainly.com/question/10426535
#SPJ1
