How do you find the integral of $\int {cos}^{2} θ$ $int cos^2theta$ ?

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How do you find the integral of $\int {cos}^{2} θ$ $int cos^2theta$ ?

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Answer 1 · 2015-09-26T03:36:11

Use the double angle formula for cosine to reduce the exponent.

Explanation:

$cos (2 θ) = 2 {cos}^{2} θ - 1$ $cos(2theta) = 2cos^2theta -1$

So ${cos}^{2} θ = \frac{1}{2} (1 + cos (2 θ))$ $cos^2theta = 1/2(1+cos(2theta))$

Hence the integral is

$\int {cos}^{2} θ d (θ) = \int \frac{1}{2} \cdot (1 + cos 2 θ) (d θ) = \frac{θ}{2} + \frac{1}{4} \cdot sin 2 θ + c$ $int cos^2theta d(theta)=int 1/2*(1+cos2theta) (d theta)= theta/2+1/4*sin2theta+c$

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How do you find the integral of $\int {cos}^{2} θ$ $int cos^2theta$ ?

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Explanation:

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How do you find the integral of $\int {cos}^{2} θ$ $int cos^2theta$ ?