Area bounded by the curve y2(2a-x) =x3 and the line x =2a is a 3a2 b 3a2/2 c - Maths - Application of Integrals

Question

Area bounded by the curve y2(2a-x) =x3 and
the line x =2a is
a 3a2
b 3a2/2
c 3a2/4
d none of these

Vipin Verma · Accepted Answer

<img alt="" src=
"https://img-nm%20mnimgs%20com/img/study_content/content_ck_images/images/1%20bmp">
Curve y2(2a-x) = x3 is symmetrical about the
x-axis and passes through the origin
So the area would be
Hence the limit is 0<x<2aSo Area = 2∫02ax3/2(2a-x)dxLet
x = 2asin2θ , so dx = 4asinθcosθOr
∫0π/28a2sin4θdθLet (sin2θ)2 =
sin4θSo (1-cos2θ2)2, so expand it, and integrate, you
will get∫sin4θdθ = (3/8)θ- (1/4)sin(2θ) +
(1/32)sin(4θ)So ∫0π/28a2sin4θdθ =
3πa2

Area bounded by the curve y2(2a-x) =x3 and the line x =2a is a. 3a2 b.3a2/2 c. 3a2/4 d. none of these

Area bounded by the curve y²(2a-x) =x³ and the line x =2a is

a. 3a²

b.3a²/2

c. 3a²/4

d. none of these