MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Definite Integral as Limit of Sum

Evaluate ∫0...

Question

Evaluate $π / 2 \int 0 \frac{c o s^{3} x}{c o s^{3} x + s i n^{3} x} d x$ .

Open in App

Solution

$I = \int_{0}^{(\frac{π}{2})} (\frac{c o s^{3} x}{c o s^{3} x + s i n^{3} x}) = \int_{0}^{(\frac{π}{2})} (\frac{c o s^{3} ((\frac{π}{2}) - x)}{c o s^{3} ((\frac{π}{2}) - x) + s i n^{3} ((\frac{π}{2}) - x)}) d x = \int_{0}^{(\frac{π}{2})} (\frac{s i n^{3} x}{s i n^{3} x + s i n^{3} x}) d x ∴ I + I = \int_{0}^{(\frac{π}{2})} (\frac{s i n^{3} x + c o s^{3} x}{s i n^{3} x + c o s^{3} x}) d x ∴ I = (\frac{1}{2}) \int_{0}^{(\frac{π}{2})} d x = (\frac{π}{4})$

Suggest Corrections

thumbs-up

0

Similar questions

\int_{0}^{π / 2} \frac{{cos}^{9} x}{{cos}^{3} x + {sin}^{3} x} d x

\int {sin}^{3} x d x + {cos}^{3} x

\int_{0}^{π} {sin}^{3} x d x

\int_{0}^{\frac{π}{2}} {sin}^{3} x d x

\int sin 3 x d x

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Definite Integral as Limit of Sum

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Definite Integral as Limit of Sum

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon