First slide

Integration

Question

Find $I = \int_{0}^{π / 4} (\sin x + \cos x) d x .$

Moderate

A

0
B

1
C

-1
D

2

Solution

$I = \int_{0}^{π / 4} (\sin x + \cos x) d x = | - \cos x + \sin x |_{0}^{π / 4} = \{- \cos (\frac{π}{4}) + \sin (\frac{π}{4})\} - {- \cos (0) + \sin (0)} = \{- \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}}\} - {- 1 + 0} = 1$

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