What is the integral from-pi/2 to pi/2 of In(cos(x)) ?

The integral from-pi/2 to pi/2 of In(cos(x)) is In*2

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integral from-pi/2 to pi/2 of In(cos(x))

\int_{- \frac{π}{2}}^{\frac{π}{2}} I n (cos (x)) d x

I n \cdot 2

Solution steps

\int_{- \frac{π}{2}}^{\frac{π}{2}} I n cos (x) d x

Take the constant out:

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

= I n \cdot \int_{- \frac{π}{2}}^{\frac{π}{2}} cos (x) d x

Use the common integral:

\int cos (x) d x = sin (x)

= I n [sin (x)]_{- \frac{π}{2}}^{\frac{π}{2}}

Compute the boundaries:

2

= I n \cdot 2

\int_{1}^{9} 10 u d u

\int_{- 1}^{1} x sin (x^{2}) d x

\int_{0}^{10} \frac{x}{16 + 2 x} d x

\int_{- 13}^{2} \frac{1}{3 - x} d x

\int_{1}^{2} 10 x^{3} + \frac{6}{x ^{2}} d x

What is the integral from-pi/2 to pi/2 of In(cos(x)) ?
The integral from-pi/2 to pi/2 of In(cos(x)) is In*2