What is the integral of-cos((pit)/4) ?

The integral of-cos((pit)/4) is -4/pi sin((pit)/4)+C

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integral of-cos((pit)/4)

\int - cos (\frac{π t}{4}) d t

- \frac{4}{π} sin (\frac{π t}{4}) + C

Solution steps

\int - cos (\frac{π t}{4}) d t

Take the constant out:

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

= - \int cos (\frac{π t}{4}) d t

Apply u-substitution

: \int cos (u) \frac{4}{π} d u

= - \int cos (u) \frac{4}{π} d u

Take the constant out:

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

= - \frac{4}{π} \cdot \int cos (u) d u

Use the common integral:

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

= - \frac{4}{π} sin (u)

Substitute back

u = \frac{π t}{4}

= - \frac{4}{π} sin (\frac{π t}{4})

Add a constant to the solution

= - \frac{4}{π} sin (\frac{π t}{4}) + C

x \to - 2 lim (- x^{2} + 6 x - 8)

\int a arctan (b x) d x

x \to 1 lim (x^{2} + 4)

y = - 0.02 x^{2} - 0.6 x + 90

\int 5 ln (x) d x

What is the integral of-cos((pit)/4) ?
The integral of-cos((pit)/4) is -4/pi sin((pit)/4)+C