What is the integral from 2 to 4 of 2cos(pix) ?

The integral from 2 to 4 of 2cos(pix) is 0

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integral from 2 to 4 of 2cos(pix)

\int_{2}^{4} 2 cos (π x) d x

0

Solution steps

\int_{2}^{4} 2 cos (π x) d x

Take the constant out:

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

= 2 \cdot \int_{2}^{4} cos (π x) d x

Apply u-substitution

= 2 \cdot \int_{π 2}^{π 4} cos (u) \frac{1}{π} d u

Take the constant out:

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

= 2 \cdot \frac{1}{π} \cdot \int_{π 2}^{π 4} cos (u) d u

Use the common integral:

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

= 2 \cdot \frac{1}{π} [sin (u)]_{π 2}^{π 4}

Simplify

2 \cdot \frac{1}{π} [sin (u)]_{π 2}^{π 4} : \frac{2}{π} [sin (u)]_{2 π}^{4 π}

= \frac{2}{π} [sin (u)]_{2 π}^{4 π}

Compute the boundaries:

0

= \frac{2}{π} \cdot 0

Simplify

= 0

What is the integral from 2 to 4 of 2cos(pix) ?
The integral from 2 to 4 of 2cos(pix) is 0