What is the integral from 0 to pi of cos^6(θ) ?

The integral from 0 to pi of cos^6(θ) is (5pi)/(16)

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integral from 0 to pi of cos^6(θ)

\int_{0}^{π} cos^{6} (θ) d θ

\frac{5 π}{16}

Decimal Notation

0.98174 \dots

Solution steps

\int_{0}^{π} cos^{6} (θ) d θ

Apply Integral Reduction

= [\frac{sin ( θ ) cos ^{5} ( θ )}{6}]_{0}^{π} + \frac{5}{6} \cdot \int_{0}^{π} cos^{4} (θ) d θ

\int_{0}^{π} cos^{4} (θ) d θ = \frac{3 π}{8}

= [\frac{sin ( θ ) cos ^{5} ( θ )}{6}]_{0}^{π} + \frac{5}{6} \cdot \frac{3 π}{8}

Simplify

[\frac{sin ( θ ) cos ^{5} ( θ )}{6}]_{0}^{π} + \frac{5}{6} \cdot \frac{3 π}{8} : [\frac{1}{6} cos^{5} (θ) sin (θ)]_{0}^{π} + \frac{5 π}{16}

= [\frac{1}{6} cos^{5} (θ) sin (θ)]_{0}^{π} + \frac{5 π}{16}

Compute the boundaries:

0

= 0 + \frac{5 π}{16}

Simplify

= \frac{5 π}{16}

\frac{d}{d x} (- \frac{1}{7})

f (x) = \frac{2 e ^{6 x - 5}}{3}

\int \frac{5}{x - 6} d x

y^{^{''}} - 2 y^{^{'}} - 3 y = 3 e^{2 t}

\int 9 + y^{2} d y

What is the integral from 0 to pi of cos^6(θ) ?
The integral from 0 to pi of cos^6(θ) is (5pi)/(16)