First slide

Evaluation of definite integrals

Question

$\int_{0}^{\frac{π}{2}} \frac{200 \sin x + 100 \cos x}{\sin x + \cos x} d x =$

Easy

A

$50 π$
B

$25 π$
C

$75 π$
D

$150 π$

Solution

$\int_{0}^{\frac{π}{2}} \frac{200 S i n x + 100 C o s x}{S i n x + C o s x} d x (\sin c e \int_{0}^{\frac{π}{2}} \frac{a S i n x + b C o s x}{S i n x + C o s x} d x = = (a + b) \frac{π}{4})$

                               $= (200 + 100) \frac{π}{4}$
                               $= 75 π$

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