What is the integral from 3pi to 4pi of cos(1/2 x) ?

The integral from 3pi to 4pi of cos(1/2 x) is 2

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integral from 3pi to 4pi of cos(1/2 x)

\int_{3 π}^{4 π} cos (\frac{1}{2} x) d x

2

Solution steps

\int_{3 π}^{4 π} cos (\frac{1}{2} x) d x

Apply u-substitution

: \int_{\frac{3 π}{2}}^{2 π} cos (u) \cdot 2 d u

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

Take the constant out:

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

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

Use the common integral:

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

= 2 [sin (u)]_{\frac{3 π}{2}}^{2 π}

Compute the boundaries:

1

= 2 \cdot 1

Simplify

= 2

\int_{- 1}^{1} (5 x + 5) d x

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

\int_{0}^{1} (7 - \frac{21}{2} x)^{2} d x

\int_{0}^{14} 8 x d x

\int_{0}^{4} 3 - \frac{x}{4} d x

What is the integral from 3pi to 4pi of cos(1/2 x) ?
The integral from 3pi to 4pi of cos(1/2 x) is 2