What is the integral from 1 to e^t of sin(x) ?

The integral from 1 to e^t of sin(x) is -cos(e^t)+cos(1)

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integral from 1 to e^t of sin(x)

\int_{1}^{e^{t}} sin (x) d x

- cos (e^{t}) + cos (1)

Solution steps

\int_{1}^{e^{t}} sin (x) d x

Use the common integral:

\int sin (x) d x = - cos (x)

= [- cos (x)]_{1}^{e^{t}}

Compute the boundaries:

- cos (e^{t}) + cos (1)

= - cos (e^{t}) + cos (1)

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