-0-2 4 sin x-3 cos x-sin x-cos xdx-

Let I=∫_0^π/2 4 sin x+3 cos x/sin x+cos xdx=∫_0^π/2 4 sin(π/2 x)+3 cos(π/2 x)/sin(π/2 x)+cos(π/2 x)dx =∫_0^π/2 4 cos x+3 sin x/sin x+cos xdx ∴ 2I=∫_0^π/2 7 sin ...

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Byju's Answer

Standard XIII

Mathematics

Inequalities of Integrals

∫0π/2 4 sin x...

Question

$\int_{0}^{\frac{π}{2}} \frac{4 s i n x + 3 c o s x}{s i n x + c o s x} d x =$

\frac{5 π}{4}

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\frac{3 π}{2}

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\frac{7 π}{4}

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\frac{5 π}{6}

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Solution

The correct option is C $\frac{7 π}{4}$
$L e t I = \int_{0}^{\frac{π}{2}} \frac{4 s i n x + 3 c o s x}{s i n x + c o s x} d x = \int_{0}^{\frac{π}{2}} \frac{4 s i n (\frac{π}{2} - x) + 3 c o s (\frac{π}{2} - x)}{s i n (\frac{π}{2} - x) + c o s (\frac{π}{2} - x)} d x$
$= \int_{0}^{\frac{π}{2}} \frac{4 c o s x + 3 s i n x}{s i n x + c o s x} d x$
$∴ 2 I = \int_{0}^{\frac{π}{2}} \frac{7 s i n x + 7 c o s x}{s i n x + c o s x} d x = 7 \int_{0}^{\frac{π}{2}} \frac{s i n x + c o s x}{s i n x + c o s x} d x = 7 [x]_{0}^{\frac{π}{2}} = \frac{7 π}{2}$
$∴ I = \frac{7 π}{4}$

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∫π20 4 sin x+3 cos xsin x+cos xdx=

The correct option is C 7π4Let I=∫π20 4 sin x+3 cos xsin x+cos xdx=∫π20 4 sin(π2−x)+3 cos(π2−x)sin(π2−x)+cos(π2−x)dx =∫π20 4 cos x+3 sin xsin x+cos xdx ∴ 2I=∫π20 7 sin x+7 cos xsin x+cos xdx=7 ∫π20 sin x+cos xsin x+cos xdx=7[x]π20=7π2 ∴ I=7π4

$\int_{0}^{\frac{π}{2}} \frac{4 s i n x + 3 c o s x}{s i n x + c o s x} d x =$