What is the integral from 0 to 100 of 37cos(x/(80)) ?

The integral from 0 to 100 of 37cos(x/(80)) is 2960sin(5/4)

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integral from 0 to 100 of 37cos(x/(80))

\int_{0}^{100} 37 cos (\frac{x}{80}) d x

2960 sin (\frac{5}{4})

Decimal

2808.99447 \dots

Solution steps

\int_{0}^{100} 37 cos (\frac{x}{80}) d x

Take the constant out:

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

= 37 \cdot \int_{0}^{100} cos (\frac{x}{80}) d x

Apply u-substitution

= 37 \cdot \int_{0}^{\frac{5}{4}} cos (u) \cdot 80 d u

Take the constant out:

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

= 37 \cdot 80 \cdot \int_{0}^{\frac{5}{4}} cos (u) d u

Use the common integral:

\int cos (u) d u = sin (u)

= 37 \cdot 80 [sin (u)]_{0}^{\frac{5}{4}}

Simplify

= 2960 [sin (u)]_{0}^{\frac{5}{4}}

Compute the boundaries:

sin (\frac{5}{4})

= 2960 sin (\frac{5}{4})

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x^{2} y^{^{''}} - 2 x y^{^{'}} - 4 y = 0, y (1) = 0, y^{^{'}} (1) = - 5

d er i v a t i v e sin^{6} (x)

\frac{d y}{d x} - 2 y = 2 x

\int t^{2} sin (2 t) d t

What is the integral from 0 to 100 of 37cos(x/(80)) ?
The integral from 0 to 100 of 37cos(x/(80)) is 2960sin(5/4)