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

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

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

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

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

Decimal Notation

1.09807 \dots

Solution steps

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

Take the constant out:

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

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

Use the common integral:

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

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

Compute the boundaries:

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

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

Simplify

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

\int_{1}^{4} - 3 x d x

\int_{1}^{2} \frac{5}{t ^{6}} d t

\int_{1}^{\infty} (\frac{1}{2})^{x} d x

\int_{1}^{3} (x - 1) (3 - x) d x

\int_{0}^{1} 1 - r^{2} d r

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