use-substitution-x-cos-2-3sin-2-show-that-1-3-dx-x-1-3-x-pi-

Question Number 44422 by peter frank last updated on 28/Sep/18

u s e s u b s t i t u t i o n x = \cos^{2} θ + 3 {s i n}^{2} θ

s h o w t h a t \int_{1}^{3} \frac{d x}{\sqrt{(x - 1) (3 - x)}} = π

Commented by maxmathsup by imad last updated on 28/Sep/18

I = \int_{0}^{\frac{π}{2}} \frac{- 2 c o s θ s i n θ + 6 s i n θ c o s θ}{\sqrt{({c o s}^{2} θ - 1 + 3 {s i n}^{2} θ) (3 - 3 {s i n}^{2} θ - {c o s}^{2} θ)}} d θ

= \int_{0}^{\frac{π}{2}} \frac{4 s i n θ . c o s θ}{\sqrt{2 {s i n}^{2} θ . 2 {c o s}^{2} θ}} d θ = 2 \int_{0}^{\frac{π}{2}} d θ = π .

Commented by peter frank last updated on 29/Sep/18

t h a n k y o u

Commented by maxmathsup by imad last updated on 29/Sep/18

y o u a r e w e l c o m e s i r .