What is the integral from 4 to 5 of xsqrt(25-x^2) ?

The integral from 4 to 5 of xsqrt(25-x^2) is 9

Popular >

integral from 4 to 5 of xsqrt(25-x^2)

\int_{4}^{5} x 25 - x^{2} d x

9

Solution steps

\int_{4}^{5} x 25 - x^{2} d x

Apply u-substitution

: \int_{9}^{0} - \frac{u}{2} d u

= \int_{9}^{0} - \frac{u}{2} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0}^{9} - \frac{u}{2} d u

Take the constant out:

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

= - (- \frac{1}{2} \cdot \int_{0}^{9} u d u)

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{9}

= - (- \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{9})

Simplify

= \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{9}

Compute the boundaries:

18

= \frac{1}{2} \cdot 18

Simplify

= 9

\int (e^{- y}) d y

\frac{( x - 8 )}{9 x ^{2} e ^{x}}

x^{^{'}} = (1 - x) \cdot 0.03 - \frac{( 0.03 x )}{( e ^{3} - 1 )}

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

\int \frac{a x}{x ^{4} + b ^{4}} d x

What is the integral from 4 to 5 of xsqrt(25-x^2) ?
The integral from 4 to 5 of xsqrt(25-x^2) is 9