By using properties of definite integrals, evaluate the integrals
$\int_{0}^{2 π} c o s^{5} x d x .$

Open in App

Solution

$\int_{0}^{2 π} c o s^{5} x d x = 2 \int_{0}^{π} c o s^{5} x d x (\begin{matrix} ∵ \int_{0}^{2 a} f (x) = 2 \int_{0}^{a} f (x) d x, w h e r e f (2 a - x) = f (x); h e n c e, 2 a = 2 x ∴ c o s^{5} (2 x - x) = c o s^{5} x \end{matrix}) = 2 \times 0 = 0 (∵ \int_{0}^{2 a} f (x) = 0, i f f (2 a - x) = - f (x); h e r e 2 a = π ∴ c o s^{5} (π - x) = - c o s^{5} x)$

Suggest Corrections

Similar questions

\int_{0}^{2 π} {cos}^{5} x d x

By using properties of definite integrals, evaluate the integrals
$\int_{0}^{1} x (1 - x)^{n} d x .$

By using properties of definite integrals, evaluate the integrals
$\int_{0}^{\frac{π}{2}} c o s^{2} d x .$

By using properties of definite integrals, evaluate the integrals
$\int_{2}^{8} | x - 5 | d x .$

By using properties of definite integrals, evaluate the integrals
$\int_{0}^{\frac{π}{2}} (2 l o g s i n x - l o g s i n 2 x) d x .$

Join BYJU'S Learning Program