What is the integral from 0 to pi/4 of 25sin^2(x) ?

The integral from 0 to pi/4 of 25sin^2(x) is (25(pi-2))/8

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integral from 0 to pi/4 of 25sin^2(x)

\int_{0}^{\frac{π}{4}} 25 sin^{2} (x) d x

\frac{25 ( π - 2 )}{8}

Decimal Notation

3.56747 \dots

Solution steps

\int_{0}^{\frac{π}{4}} 25 sin^{2} (x) d x

Take the constant out:

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

= 25 \cdot \int_{0}^{\frac{π}{4}} sin^{2} (x) d x

Rewrite using trig identities

= 25 \cdot \int_{0}^{\frac{π}{4}} \frac{1 - cos ( 2 x )}{2} d x

Take the constant out:

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

= 25 \cdot \frac{1}{2} \cdot \int_{0}^{\frac{π}{4}} 1 - cos (2 x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 25 \cdot \frac{1}{2} (\int_{0}^{\frac{π}{4}} 1 d x - \int_{0}^{\frac{π}{4}} cos (2 x) d x)

\int_{0}^{\frac{π}{4}} 1 d x = \frac{π}{4}

\int_{0}^{\frac{π}{4}} cos (2 x) d x = \frac{1}{2}

= 25 \cdot \frac{1}{2} (\frac{π}{4} - \frac{1}{2})

Simplify

25 \cdot \frac{1}{2} (\frac{π}{4} - \frac{1}{2}) : \frac{25 ( π - 2 )}{8}

= \frac{25 ( π - 2 )}{8}

\frac{d}{d x} (\frac{3 ^{x}}{ln ( 3 )})

x \to 0 lim (\frac{x}{x ^{2} - 7 x + 1})

y^{^{'}} = \frac{x ^{2} y - y}{y + 1}

\int 2 x - 5 d x

x \to 2 lim ((3 - x)^{2})

What is the integral from 0 to pi/4 of 25sin^2(x) ?
The integral from 0 to pi/4 of 25sin^2(x) is (25(pi-2))/8