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

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

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

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

1

Solution steps

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

Apply u-substitution

: \int_{0}^{1} 1 d u

= \int_{0}^{1} 1 d u

Integral of a constant:

\int a d x = a x

= [1 \cdot u]_{0}^{1}

Simplify

= [u]_{0}^{1}

Compute the boundaries:

1

= 1

\int_{- 1}^{2} 3 x d x

\int_{0}^{2} \frac{x ^{2}}{4} d x

\int_{0}^{4} x^{3} - 6 x^{2} + 8 x d x

\int_{0}^{1} \frac{x + 1}{4 + x ^{2}} d x

\int_{3}^{4} x d x

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