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

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

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

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

3 (3 - 1)

Decimal Notation

2.19615 \dots

Solution steps

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

Take the constant out:

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

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

Use the common integral:

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

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

Compute the boundaries:

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

= 6 (\frac{3}{2} - \frac{1}{2})

Simplify

= 3 (3 - 1)

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

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

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