integral from pi to 5pi of x^2sin(x)

解答

\int_{π}^{5 π} x^{2} sin (x) d x

24 π^{2}

十进制

236.87050 \dots

求解步骤

\int_{π}^{5 π} x^{2} sin (x) d x

使用分布积分法

= [- x^{2} cos (x) - \int - 2 x cos (x) d x]_{π}^{5 π}

\int - 2 x cos (x) d x = - 2 (x sin (x) + cos (x))

= [- x^{2} cos (x) - (- 2 (x sin (x) + cos (x)))]_{π}^{5 π}

化简

= [- x^{2} cos (x) + 2 (x sin (x) + cos (x))]_{π}^{5 π}

带入上下限计算后得:

24 π^{2}

= 24 π^{2}

t a y l or 3 + 4 x^{2} - 5 x^{3}

\int \frac{1}{1 + \frac{x}{2}} d x

n = 1 \sum \infty \frac{3 ^{n}}{4 ^{n + 1}}

x \to 1 lim (4 x - 1)

d er i v a t i v e \frac{150000}{( 4 t + 75 ) ^{2}}