How to evaluate the definite integral (0,1) ∫ cos(πt/2)dt ?

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How to evaluate the definite integral (0,1) ∫ cos(πt/2)dt ?

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Answer 1 · 2015-09-24T21:16:37

Refer to explanation

Explanation:

Set $u = π \cdot \frac{t}{2} \Rightarrow d u = \frac{π}{2} d t$ $u=pi*t/2=>du=pi/2dt$ and integration limits are

$t = 1 \Rightarrow u = \frac{π}{2}$ $t=1=>u=pi/2$ and $t = 0 \Rightarrow u = 0$ $t=0=>u=0$ hence the integral becomes

$\int_{0}^{\frac{π}{2}} (\frac{2}{π}) \cdot cos u d u = (\frac{2}{π}) \cdot {[sin]}_{0}^{\frac{π}{2}} = \frac{2}{π}$ $int_0^(pi/2) (2/pi)*cosudu=(2/pi)*[sin]_0^(pi/2)=2/pi$

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How to evaluate the definite integral (0,1) ∫ cos(πt/2)dt ?

1 Answer

Explanation:

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