What is the integral from 0 to pi/4 of 1/(1+cos(2x)) ?

The integral from 0 to pi/4 of 1/(1+cos(2x)) is 1/2

Popular >

integral from 0 to pi/4 of 1/(1+cos(2x))

\int_{0}^{\frac{π}{4}} \frac{1}{1 + cos ( 2 x )} d x

\frac{1}{2}

Decimal

0.5

Solution steps

\int_{0}^{\frac{π}{4}} \frac{1}{1 + cos ( 2 x )} d x

Rewrite using trig identities

= \int_{0}^{\frac{π}{4}} \frac{1}{2 cos ^{2} ( x )} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int_{0}^{\frac{π}{4}} \frac{1}{cos ^{2} ( x )} d x

Use the common integral:

\int \frac{1}{cos ^{2} ( x )} d x = tan (x)

= \frac{1}{2} [tan (x)]_{0}^{\frac{π}{4}}

Compute the boundaries:

1

= \frac{1}{2} \cdot 1

Simplify

= \frac{1}{2}

\int_{1}^{3} π (- x^{2} + 4 x - 3)^{2} d x

\int_{- 32}^{32} 5 x^{8} d x

\int_{- 1}^{1} u^{5} d u

\int_{- \infty}^{1} \frac{x}{x ^{2} + 1} d x

\int_{0}^{4} (x + e^{- x}) d x

What is the integral from 0 to pi/4 of 1/(1+cos(2x)) ?
The integral from 0 to pi/4 of 1/(1+cos(2x)) is 1/2