Calculus UNIT501 HWK p294 -- Sage

#20) integrate(cos(x),x)

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

integrate(cos(x),x,0,pi/2)

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

plot(cos(x),0,pi/2,aspect_ratio=1)

#30) integrate(-x^(-2),x)

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

integrate(-x^(-2),x,1,4)

 $\newcommand{\Bold}[1]{\mathbf{#1}}-\frac{3}{4}$

plot(-1/x^2,1,4,aspect_ratio=1)

#15) integrate(x+4,x)

 $\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{2} \, x^{2} + 4 \, x$

integrate(-x+2,x)

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

integrate(x+4,x,-4,-1)

 $\newcommand{\Bold}[1]{\mathbf{#1}}\frac{9}{2}$

integrate(-x+2,x,-1,2)

 $\newcommand{\Bold}[1]{\mathbf{#1}}\frac{9}{2}$

integrate(x+4,x,-4,-1)+integrate(-x+2,x,-1,2)

 $\newcommand{\Bold}[1]{\mathbf{#1}}9$

f1(x)=x+4 f2(x)=-x+2 f=piecewise([[(-4,-1),f1],[(-1,2),f2]]) plot(f,aspect_ratio=1)

(1/2)*(6)*(3)

 $\newcommand{\Bold}[1]{\mathbf{#1}}9$

Calculus UNIT501 HWK p294