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

The integral from (-pi)/2 to a of cos(4x) is 1/4 sin(4a)

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integral from (-pi)/2 to a of cos(4x)

\int_{\frac{- π}{2}}^{a} cos (4 x) d x

\frac{1}{4} sin (4 a)

Solution steps

\int_{\frac{- π}{2}}^{a} cos (4 x) d x

Apply u-substitution

: \int_{- 2 π}^{4 a} cos (u) \frac{1}{4} d u

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

Take the constant out:

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

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

Use the common integral:

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

= \frac{1}{4} [sin (u)]_{- 2 π}^{4 a}

Compute the boundaries:

sin (4 a)

= \frac{1}{4} sin (4 a)

\int_{0}^{\frac{π}{2}} e^{- x} sin (2 x) d x

\int_{0}^{π} x cos (\frac{x}{2}) d x

\int_{0}^{30} x^{2} e^{- x} d x

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

\int_{17}^{21} x d x

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