What is the integral from 0 to x of (3+sin(t)) ?

The integral from 0 to x of (3+sin(t)) is 3x-cos(x)+1

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integral from 0 to x of (3+sin(t))

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

3 x - cos (x) + 1

Solution steps

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

\int_{0}^{x} 3 d t = 3 x

\int_{0}^{x} sin (t) d t = - cos (x) + 1

= 3 x - cos (x) + 1

What is the integral from 0 to x of (3+sin(t)) ?
The integral from 0 to x of (3+sin(t)) is 3x-cos(x)+1