What is the integral from pi/6 to pi/3 of 2cos(x) ?

The integral from pi/6 to pi/3 of 2cos(x) is sqrt(3)-1

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integral from pi/6 to pi/3 of 2cos(x)

\int_{\frac{π}{6}}^{\frac{π}{3}} 2 cos (x) d x

3 - 1

Decimal Notation

0.73205 \dots

Solution steps

\int_{\frac{π}{6}}^{\frac{π}{3}} 2 cos (x) d x

Take the constant out:

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

= 2 \cdot \int_{\frac{π}{6}}^{\frac{π}{3}} cos (x) d x

Use the common integral:

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

= 2 [sin (x)]_{\frac{π}{6}}^{\frac{π}{3}}

Compute the boundaries:

\frac{3}{2} - \frac{1}{2}

= 2 (\frac{3}{2} - \frac{1}{2})

Simplify

= 3 - 1

\int_{0}^{3} x^{3} + 5 d x

\int_{0}^{0.5} \frac{4}{3} (1 - x^{3}) d x

\int_{0}^{x} 2 (x + y) d y

\int_{x}^{1} \frac{32}{9} (x y)^{\frac{1}{3}} d y

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

What is the integral from pi/6 to pi/3 of 2cos(x) ?
The integral from pi/6 to pi/3 of 2cos(x) is sqrt(3)-1