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

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

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integral from 0 to 3 of-3cos(t)+1

\int_{0}^{3} - 3 cos (t) + 1 d t

- 3 sin (3) + 3

Decimal Notation

2.57663 \dots

Solution steps

\int_{0}^{3} - 3 cos (t) + 1 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}^{3} 3 cos (t) d t + \int_{0}^{3} 1 d t

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

\int_{0}^{3} 1 d t = 3

= - 3 sin (3) + 3

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