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

Question

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

1 Answer

Related questions

How do I evaluate the indefinite integral $\int {sin}^{3} (x) \cdot {cos}^{2} (x) d x$ $intsin^3(x)*cos^2(x)dx$ ?
How do I evaluate the indefinite integral $\int {sin}^{6} (x) \cdot {cos}^{3} (x) d x$ $intsin^6(x)*cos^3(x)dx$ ?
How do I evaluate the indefinite integral $\int {cos}^{5} (x) d x$ $intcos^5(x)dx$ ?
How do I evaluate the indefinite integral $\int {sin}^{2} (2 t) d t$ $intsin^2(2t)dt$ ?
How do I evaluate the indefinite integral $\int {(1 + cos (x))}^{2} d x$ $int(1+cos(x))^2dx$ ?
How do I evaluate the indefinite integral $\int {sec}^{2} (x) \cdot tan (x) d x$ $intsec^2(x)*tan(x)dx$ ?
How do I evaluate the indefinite integral $\int {cot}^{5} (x) \cdot {sin}^{4} (x) d x$ $intcot^5(x)*sin^4(x)dx$ ?
How do I evaluate the indefinite integral $\int {tan}^{2} (x) d x$ $inttan^2(x)dx$ ?
How do I evaluate the indefinite integral $\int {({tan}^{2} (x) + {tan}^{4} (x))}^{2} d x$ $int(tan^2(x)+tan^4(x))^2dx$ ?
How do I evaluate the indefinite integral $\int x \cdot sin (x) \cdot tan (x) d x$ $intx*sin(x)*tan(x)dx$ ?

Impact of this question

71518 views around the world

You can reuse this answer
Creative Commons License

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

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

Science

Math

Humanities

... and beyond

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

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you find the integral of int cos^2theta∫cos2θint cos^2theta?

1 Answer

Explanation:

Related questions

Impact of this question

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