What is the integral from 0 to pi/2 of (5cos(x))/(sqrt(sin(x))) ?

The integral from 0 to pi/2 of (5cos(x))/(sqrt(sin(x))) is 10

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integral from 0 to pi/2 of (5cos(x))/(sqrt(sin(x)))

\int_{0}^{\frac{π}{2}} \frac{5 cos ( x )}{sin ( x )} d x

10

Solution steps

\int_{0}^{\frac{π}{2}} \frac{5 cos ( x )}{sin ( x )} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int_{0}^{\frac{π}{2}} \frac{cos ( x )}{sin ( x )} d x

Apply u-substitution

: \int_{0}^{1} \frac{1}{u} d u

= 5 \cdot \int_{0}^{1} \frac{1}{u} d u

Apply the Power Rule

: [2 u^{\frac{1}{2}}]_{0}^{1}

= 5 [2 u^{\frac{1}{2}}]_{0}^{1}

Apply radical rule:

= 5 [2 u]_{0}^{1}

Compute the boundaries:

2

= 5 \cdot 2

Simplify

= 10

\frac{d y}{d t} = \frac{4 t ^{8}}{e + t ^{9}}

\frac{d}{d x} (\frac{- 2}{( x - 1 ) ^{2}})

y^{^{'}} = e^{5 x} - 9 x

\frac{\partial}{\partial x} (y + 2)

\frac{d}{d x} (2 x^{3} - 6 x)

What is the integral from 0 to pi/2 of (5cos(x))/(sqrt(sin(x))) ?
The integral from 0 to pi/2 of (5cos(x))/(sqrt(sin(x))) is 10