What is the integral from 0 to 4 of cos(sqrt(x)-1) ?

The integral from 0 to 4 of cos(sqrt(x)-1) is 2cos(1)(2sin(2)+cos(2)-1)+2sin(1)(sin(2)-2cos(2))

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integral from 0 to 4 of cos(sqrt(x)-1)

\int_{0}^{4} cos (x - 1) d x

2 cos (1) (2 sin (2) + cos (2) - 1) + 2 sin (1) (sin (2) - 2 cos (2))

Decimal Notation

3.36588 \dots

Solution steps

\int_{0}^{4} cos (x - 1) d x

Rewrite using trig identities

= \int_{0}^{4} cos (x) cos (1) + sin (x) sin (1) d x

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}^{4} cos (x) cos (1) d x + \int_{0}^{4} sin (x) sin (1) d x

\int_{0}^{4} cos (x) cos (1) d x = 2 cos (1) (2 sin (2) + cos (2) - 1)

\int_{0}^{4} sin (x) sin (1) d x = 2 sin (1) (sin (2) - 2 cos (2))

= 2 cos (1) (2 sin (2) + cos (2) - 1) + 2 sin (1) (sin (2) - 2 cos (2))

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\int_{1}^{5} \frac{1}{x - 3} d x

What is the integral from 0 to 4 of cos(sqrt(x)-1) ?
The integral from 0 to 4 of cos(sqrt(x)-1) is 2cos(1)(2sin(2)+cos(2)-1)+2sin(1)(sin(2)-2cos(2))