Calculus UNIT501 What's an AnitDerivative? -- Sage

f(x)=cos(x) integrate(f(x),x)

 $\newcommand{\Bold}[1]{\mathbf{#1}}\sin\left(x\right)$

f(x)=cos(2*x) integrate(f(x),x)

 $\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{2} \, \sin\left(2 \, x\right)$

f(x)=3*x^2 integrate(f(x),x)

 $\newcommand{\Bold}[1]{\mathbf{#1}}x^{3}$

f(x)=1/(2*sqrt(x)) integrate(f(x),x)

 $\newcommand{\Bold}[1]{\mathbf{#1}}\sqrt{x}$

f(x)=1/x^2 integrate(f(x),x)

 $\newcommand{\Bold}[1]{\mathbf{#1}}-\frac{1}{x}$

f(x)=2 integrate(f(x),x)

 $\newcommand{\Bold}[1]{\mathbf{#1}}2 \, x$

f(x)=10*x+2 integrate(f(x),x)

 $\newcommand{\Bold}[1]{\mathbf{#1}}5 \, x^{2} + 2 \, x$

f(x)=-x^2+10*x+2 integrate(f(x),x)

 $\newcommand{\Bold}[1]{\mathbf{#1}}-\frac{1}{3} \, x^{3} + 5 \, x^{2} + 2 \, x$

f(x)=sqrt(x) integrate(f(x),x)

 $\newcommand{\Bold}[1]{\mathbf{#1}}\frac{2}{3} \, x^{\frac{3}{2}}$

f(x)=1/sqrt(x) integrate(f(x),x)

 $\newcommand{\Bold}[1]{\mathbf{#1}}2 \, \sqrt{x}$

f(x)=6*cos(2*x) integrate(f(x),x)

 $\newcommand{\Bold}[1]{\mathbf{#1}}3 \, \sin\left(2 \, x\right)$

f(x)=5*cos(x/2) integrate(f(x),x)

 $\newcommand{\Bold}[1]{\mathbf{#1}}10 \, \sin\left(\frac{1}{2} \, x\right)$

f(x)=cos(2*pi*x) integrate(f(x),x)

 $\newcommand{\Bold}[1]{\mathbf{#1}}\frac{\sin\left(2 \, \pi x\right)}{2 \, \pi}$

var('g') a(t)=g integrate(a(t),t)

 $\newcommand{\Bold}[1]{\mathbf{#1}}g t$

var('v0') v(t)=g*t+v0 integrate(v(t),t)

 $\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{2} \, g t^{2} + t v_{0}$

var('s0') s(t)=g*t^2/2+v0*t+s0 show(s(t)) v(t)=diff(s(t),t) show(v(t)) a(t)=diff(v(t),t) show(a(t))

 $\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{2} \, g t^{2} + t v_{0} + s_{0}$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}g t + v_{0}$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}g$

Calculus UNIT501 What's an AnitDerivative?

2962 days ago by MATH4R2013