What is the integral of 4000+2000sin((pit)/(90)) ?

The integral of 4000+2000sin((pit)/(90)) is 4000t-(180000)/pi cos((pit)/(90))+C

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integral of 4000+2000sin((pit)/(90))

\int 4000 + 2000 sin (\frac{π t}{90}) d t

4000 t - \frac{180000}{π} cos (\frac{π t}{90}) + C

Solution steps

\int 4000 + 2000 sin (\frac{π t}{90}) d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 4000 d t + \int 2000 sin (\frac{π t}{90}) d t

\int 4000 d t = 4000 t

\int 2000 sin (\frac{π t}{90}) d t = - \frac{180000}{π} cos (\frac{π t}{90})

= 4000 t - \frac{180000}{π} cos (\frac{π t}{90})

Add a constant to the solution

= 4000 t - \frac{180000}{π} cos (\frac{π t}{90}) + C

\frac{4 s}{s ^{2} - 1}

\int 10 x 5 x^{2} - 4 d x

\int_{0}^{x^{3}} sin (t) d t

x \to - 5 + lim (ln (x + 5))

\frac{s + 5}{( s + 3 ) ( s - 1 )}

What is the integral of 4000+2000sin((pit)/(90)) ?
The integral of 4000+2000sin((pit)/(90)) is 4000t-(180000)/pi cos((pit)/(90))+C