What is the integral from 0 to 1.5 of e^{-x}cos(x) ?

The integral from 0 to 1.5 of e^{-x}cos(x) is 0.60339…

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integral from 0 to 1.5 of e^{-x}cos(x)

\int_{0}^{1.5} e^{- x} cos (x) d x

0.60339 \dots

Solution steps

\int_{0}^{1.5} e^{- x} cos (x) d x

Compute the indefinite integral:

\int e^{- x} cos (x) d x = \frac{e ^{- x} sin ( x )}{2} - \frac{e ^{- x} cos ( x )}{2} + C

Compute the boundaries:

\int_{0}^{1.5} e^{- x} cos (x) d x = 0.10339 \dots - (- \frac{1}{2})

= 0.10339 \dots - (- \frac{1}{2})

Simplify

= 0.60339 \dots

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What is the integral from 0 to 1.5 of e^{-x}cos(x) ?
The integral from 0 to 1.5 of e^{-x}cos(x) is 0.60339…