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

\int_{11}^{30} - 0.8 x + 30 d x

\int_{0}^{3} \frac{1}{96} y^{3} e^{- \frac{y}{2}} d y

\int_{0}^{0.9} \frac{cos ( x ) - 1}{x} d x

\int_{0}^{1} \frac{1}{( x + y + 1 ) ^{2}} d x

\int_{- \frac{π}{2}}^{\frac{π}{2}} sin^{2} (t) d t

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