What is the integral from 0 to pi/6 of 12cos(x) ?

The integral from 0 to pi/6 of 12cos(x) is 6

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integral from 0 to pi/6 of 12cos(x)

\int_{0}^{\frac{π}{6}} 12 cos (x) d x

6

Solution steps

\int_{0}^{\frac{π}{6}} 12 cos (x) d x

Take the constant out:

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

= 12 \cdot \int_{0}^{\frac{π}{6}} cos (x) d x

Use the common integral:

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

= 12 [sin (x)]_{0}^{\frac{π}{6}}

Compute the boundaries:

\frac{1}{2}

= 12 \cdot \frac{1}{2}

Simplify

= 6

\int_{0}^{1} π (y)^{2} d y

\int_{0}^{x} \frac{6}{1 + 6 x ^{2}} d x

\int_{0}^{2} 3 x - 1 d x

\int_{0}^{4} 5 x^{2} + 3 x + 1 d x

\int_{0}^{8} (x^{2} - 5) d x

What is the integral from 0 to pi/6 of 12cos(x) ?
The integral from 0 to pi/6 of 12cos(x) is 6